Abstract

We propose a specific method for converting a four-photon Greenberger-Horne-Zeilinger (GHZ) state to a W state in a deterministic way by using linear optical elements, cross-Kerr nonlinearities, and homodyne measurement. We consider the effects of the quadrature homodyne measurements on the fidelity of the W state and the experimental feasibility of the proposed scheme. This might provide great prospects for converting multipartite entangled states into each other for future optical quantum information processing (QIP).

© 2016 Optical Society of America

1. Introduction

Quantum entanglement is one of the most important resources of QIP task, such as quantum teleportation [1,2], quantum key distribution (QKD) [3,4], quantum secret sharing [5,6], quantum secure direct communication (QSDC) [7, 8], etc.. Although the property of entanglement has been well understood for bipartite system, the entanglement of multipartite system is also appealing and the preparation and application of multipartite entanglement has attracted much attention. For a multipartite system, the two most common classes of entangled states are the W state and the Greenberger-Horne-Zeilinger (GHZ) state, which are impossible to convert a GHZ state into an W state only by local operations and classical communication (LOCC) [9,10]. For GHZ state, which plays a crucial role in engineering entanglement [11, 12], quantum secret sharing [13] and hyperentanglement concentration [14], the entanglement completely destroys with the loss of any one of the qubits. However, the W state is robust against the loss of one qubit, that is, the remaining qubits can be still entangled with each other when one qubit is discarded [9]. Therefore, the W state as a resource is widely used in the development of quantum computing and quantum information science [15, 16]. Recently, some studies have sought to implement the conversion between GHZ state and W state. In 2005, Walther et al. described a probabilistic method to convert a GHZ state into an approximate W state based on partial quantum measurement (POVMs) and experimentally realized the scheme in the 3-qubit case [17]. In 2009, Tashima et al. proposed and experimentally demonstrated how to transform two Einstein-Podolsky-Rosen Photon pairs into a three-photon W state [18]. Then we propsoed a scheme for converting four EPR photon pairs distributed among five parties into the heralded four-photon polarization-entangled decoherence-free states via LOCC [19]. In 2013, Song et al. proposed a scheme for converting a four-atom W state to a Greenberger-Horne-Zeilinger state via a dissipative process [20]. All these two classes of entangled states can perform different tasks in QIP, and there have been many experimental realizations on the preparation of GHZ state and more about W state [21, 22]. Naturally, the question wether it is possible to convert a GHZ state into an exact W state deterministically thus arises.

It is well known that photons are ideal quantum information carrier as they travel with high speed and are negligibly affected by decoherence. Qubit is usually encoded on the vertical polarization and horizontal polarization states of photons, and quantum information tasks can be achieved by using linear optical elements. However, as the probabilistic nature of linear optical quantum gates, the quantum information tasks can not be achieved deterministically in linear optical system. Cross-Kerr nonlinearity is a promising way for deterministic optical QIP. In 1995, Chuang and Yamamoto [23] first proposed an implementation of a quantum computer to solve Deutsch’s problem and realize error correction with the cross-Kerr nonlinearity. In 2003, Munro et al. [24] proposed a scheme for a highly efficient photon-number quantum-nondemolition detector (QND) with single-photon resolving based on the cross-Kerr nonlinearity. Due to strong Kerr nonlinearities are difficult to achieve in experiment, in their follow-on work, they realized nearly deterministic quantum gate with strong coherent state and weak-Kerr nonlinearity with electromagnetically induced transparency (EIT) [24–27]. Recently, more and more schemes for QIP have been proposed with cross-Kerr nonlinearities [28–32]. Our scheme is basd on the cross-Kerr nonlinearity that having a brief rundown of the cross-Kerr nonlinear interaction between probe mode and signal mode is needed, as shown in Fig. 1. The interaction Hamiltonian using creation and annihilation operators can be written as [33]

H^QND=h¯χa^sa^sa^pa^p.
where as(ap) and âs (âp) represent the creation and annihilation operators of the signal mode (probe mode), χ is the nonlinearity strengh. Consider a coherent beam in the state |α〉 with a signal pulse in the Fock state |Φ〉 = a|0〉 + b|1〉. Here, |0〉 and |1〉 represent the number of the photons. After interaction with the cross-Kerr interaction medium, the state evolves as
Uck|Φ|α=eiH^QNDt/h¯(a|0+b|1)|α=a|0|α+b|1|αeiθ.
where θ = χt and t is the interaction time. From Eq. (2), it is obvious that the signal photon state is unaffected after the interaction, but the coherent state picks up a θ phase shift directly proportional to the number of the photons in the signal mode. So, the photon numbers in signal mode can be distinguished through the measurement on the phase of probe beam.

 figure: Fig. 1

Fig. 1 Cross-Kerr nonlinear interaction model.

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2. Converting a four-photon GHZ state to a W state

In this section, we illustrate how to convert a four-photon GHZ state to a W state in a deterministic way by using cross-Kerr nonlinearities, linear optics elements, and homodyne measurement. The schematic setup is shown in Fig. 2. Assume that four photons are initially prepared in the GHZ state

|ϕ0=12(|H1|H2|H3|H4+|V1|V2|V3|V4).
In the FS basis representation, the state in Eq. (3) is rewritten as
|ϕ0=122(|F1|F2|F3|F4+|F1|S2|F3|S4+|S1|F2|F3|S4+|S1|S2|F3|F4+|F1|F2|S3|S4+|F1|S2|S3|F4+|S1|F2|S3|F4+|S1|S2|S3|S4)|α.
where |F〉 and |S〉 are the superposition of horizontal and vertical polarization states [34], namely, |F=1/2(|H+|V) and |S=1/2(|H|V).

 figure: Fig. 2

Fig. 2 Schematic diagram for conversion from a GHZ state to a W state. And the qubit flip (QF) device is composed of two HV-PBS and a phase shifter (PS). Here, the FS-PBS, which transmits F-polarized photons and reflects S-polarized photons is the polarizing beam splitter (PBS) in the |F〉 and |S〉 basis. HV-PBS, which transmits H-polarized photons and reflects V-polarized photons, is the PBS in the in the |H〉 and |V〉 basis. PS denotes a phase shifter, which is to realize the transformation: |H〉 → |H〉, |V〉 → −|V〉.

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The photons in modes 1, 2, 3, 4 respectively pass through a FS-PBS, which transmits F-polarized photons and reflects S-polarized photons. Then the photon in modes 1′ passes through a qubit-flip (QF) device, which is to complete the transformation {|F〉 → |S〉, |S〉 → |F〉}. Next the |F〉 polarization states of photons in modes a′, b′, c′, d′ interacts with cross-Kerr nonlinearities, respectively. After the photons pass through the remaining FS-PBS, the whole system is evolved into the following state

|ϕ2=122[(|Sa|Fb|Fc|Fd+|Fa|Sb|Fc|Sd+|Sa|Fb|Sc|Sd+|Fa|Fb|Fc|Sd)+|αe3θ+(|Fa|Sb|Sc|Sd+|Sa|Fb|Fc|Fd+|Sa|Sb|Fc|Sd+|Sa|Sb|Sc|Fd)|αeθ].
We now take advantage of X-quadrature homodyne measurement [35, 36] which will project the probe mode to position space. With α real, the state as shown in Eq. (5) will be collapsed to
|ϕXX|ϕ3=1N[2f(x,αcos3θ)eiϕ(X)1|φ1+2f(x,αcosθ)eiφ(X)2|φ2],
where
f(x,β)=exp[14(x2β)2]/(2π)1/4,ϕ(X)1=αsin3θ(x2αcos3θ)Mod2π,ϕ(X)2=αsinθ(x2αcosθ)Mod2π,|φ1=12(|Sa|Fb|Fc|Fd+|Fa|Sb|Fc|Sd+|Fa|Fb|Sc|Fd+|Fa|Fb|Fc|Sd),|φ2=12(|Fa|Sb|Sc|Sd+|Sa|Fb|Sc|Sd+|Sa|Sb|Fc|Sd+|Sa|Sb|Sc|Fd),N[4f2(x,αcos3θ)+4f2(x,αcosθ)]1/2.
With the homodyne measurement of the state of Eq. (5), the conversion from a four-photon GHZ state to a four-photon W state is achieved deterministically, with the probability of success of 1.0.

3. Discussion

In this section, we first discuss the effects of X-quadrature homodyne measurement on the fidelity of the W state and the experimental feasibility of the proposed scheme. To qualify the performance of the present scheme, we plot the effects of homodyne measurement on the fidelity of the converted W state, as shown in Fig. 3. One can see from Fig. 3(a) that the fidelity of the W state increases with the increase of the amplitude of coherent state α and the increase of the phase shift angle θ, here we set δ = 10. In Fig. 3(b), we can see that the fidelity of the W state increases with the increase of the amplitude of coherent state α, but decreases with increasing the distance between the measurement result and the peak δ, here we set θ = 0.01. Figure 3(c) shows that the fidelity of the W state increases with the increase of the phase shift angle θ, while decreases with the increase of the distance between the measurement result and the peak δ, here we set α = 40000. In the following we consider f(x, αcos) (n = 1, 3) as a function of the position component x, and the curves of f(x, αcos) is shown in Fig. 4. It is totally to see that f(x, αcos) are Gaussian curves with the peak located at 2αcos. The distance of the two peaks are 2d = 2α(cosθ − cos3θ), which are commonly reported as the distinguish abilities of the homodyne measurement [37]. We make a detailed analysis that the result of the homodyne measurement x is near the peak of 2 f(x, αcos3θ). Without loss of generality, we consider that the result of measurement is x1 = 2αcos3θ + δ1. In this case, the W state in Eq. (6) will be projected to |φ1, with the fidelity

F(X1)=|φ|ϕ1X|11+e2d1(d1δ1),
from which one could calculate the fidelity easily if the value of α and θ are given out. For example, setting θ = 0.01 and α = 40000, it can be obtained that F(x1) = 0.9999 with δ1 ≈ 0.9958d1.

 figure: Fig. 3

Fig. 3 (a) The effects of the homodyne measurement on the fidelity of the W state versus the amplitude of coherent state α and the distance between the measurement results and the phase shift angle θ, here we set δ = 10. (b) The effects of the homodyne measurement on the fidelity of the W state versus the amplitude of coherent state α and the distance between the measurement results and the peak δ, here we set θ = 0.01. (c) The effects of the homodyne measurement on the fidelity of the W state versus the phase shift angle θ and the distance between the measurement results and the peak δ, here we set α = 40000.

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 figure: Fig. 4

Fig. 4 Curves of the homodyne measurement result X with α = 40000 and θ = 0.01.

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The small overlap between two adjacent Gaussian cures is shown in Fig. 4, f(x, αcosθ) and f(x, α cos3θ), amount to the error rate of the homodyne measurement. The error probability is given by Perror=12erfc([d/22]) [36], here d is the distance between the adjacent curves. setting α = 40000 and θ = 0.01, Perror with an approximate value equals to 10−16, which indicates that the probability of success approaches to unity. This shows that it is still possible to operate in the regime of weak cross-Kerr nonlinearity.

In what follows, we analyze and discuss the decoherence in our scheme based on the weak cross-Kerr nonlinearity. In ideal circumstances, the output state of the W state should be the pure entangled state. With the decoherence effects in the nonlinear media, however, the realistic outcome state will be a mixed state. There are two reasons for the photon losses, which may occur both in the probe filed (p) and in the signal modes (1, 2, 3, and 4). One can see that the probability of the photon losses in signal modes becomes lower with the increase of the initial amplitude because the interaction time t = θ/χ becomes shorter. Therefore, it is necessary to consider the factor of losing photons in the probe filed mode. The master equation of decoherence effects for describing dissipation is as follows [38]

ρt=J^ρ+L^ρ,J^ρ=γaρa,L^ρ=γ2(aaρ+ρaa).
where a and a denote the annihilation and creation operators of the coherent state, γ is the decay constant, and ρ represents the density matrix of the system. The formal solution of the master equation (9) can be described as ρ(t) = (t)ρ(0), where D˜(t)=exp[(J^+L^)t]=exp(L^t)exp[J^γ1eγt] is the decoherence superoperator. We should note that the decoherence process ((t)) caused by the nonlinear interaction between photons and the coherent state are companied with a unitary evolution (Ũ(t)), which can be given by Ũ(t)ρ (0)= U(t)ρ (0)U(t), where U(t) is the unitary superoperator. We assume that the Ũ and alternately and continuously execute on the system with a short time Δt = t/N, i.e., the interval t is divided into N (N ∼ ∞) parts. As mentioned above, we consider the evolution of the initial state of the system |ϕ1, and the system evolves to [39–41]
ρ(t)=[D˜(Δt)U˜(Δt)]Nρ(0)=j,k=1,3eBj,k(|ϕjϕk|)|AaeijθAaeikθ|,
with
A=γt/2,Bj,k=α2(1A2N)n=1NA2(n1)N[ei(Jk)nθN1].
where the j, k represent the multiple of θ. It is clear from the Eq. (10) that the photon losses in the probe filed mode reduce its amplitude and also lead the original pure state to a mixed state, with the homodyne measurement of the dissipated coherence state, which can be described by
|xρ(t)x|=j,k=1,3Cj,k(|ϕjϕk|)f(x,jθ)f(x,kθ)ei[μjk+φ(x,jθ)φ(x,kθ)],
where
Cj,k=eRe(Bjk),μjk=Im(Bjk),f(x,nθ)=exp[14(x2Aαcosnθ)2)]/(2π)1/4(n=1,3),φ(x,nθ)=(x2Aαcosnθ)Aαsinnθ(n=1,3).
Then we consider the partial overlap between two adjacent Gaussian curves inducing a measurement error rate and the fidelity of the output state, which is similar to that discussed earlier. Here the decoherence coefficient A should be taken into account, as shown in Fig. 5. In Fig. 5(a), we plot the measurement error rate Perror versus the decoherence coefficient A and the amplitude α of the coherent state. It would seem obviously that the measurement error rate decreases with the increase of the the decoherence coefficient A and the amplitude α of the coherent state, where we set θ = 0.01. If setting α = 40000, A = 0.9, Perror ≈ 10−13; α = 40000, A = 0.5, Perror ≈ 10−5, and the two measurement outcomes can be distinguished with the error rate less than 10−4. Figure 5(b) shows the fidelity which are the function of the decoherence coefficient A and the amplitude α of the coherent state, where we set δ = 0.1d1, θ = 0.01. One can see that the fidelity of the process of X-quadrature homodyne measurement increases with the increase of the decoherence coefficient A and the amplitude α of the coherent state. By calculation, we obtain that α = 40000, A = 0.5, F = 0.9999; α = 60000, A = 0.3, F = 0.9999, that is to say, the amplitude α of the coherent state can make up for the influence from the decoherence coefficient A.

 figure: Fig. 5

Fig. 5 (a) The measurement error rate versus the decoherence coefficient A and the amplitude α of the coherent state, here we set θ = 0.01. (b) The fidelity of the output state versus the decoherence coefficient A and the amplitude α of the coherent state, where we set the δ = 0.1d1, θ = 0.01.

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On the other hand, the feasibility of the present scheme depends on the cross-Kerr medium, X-quadrature homodyne measurement, and linear optical elements. In practice, the nonlinearity of cross-Kerr medium is extremely small with θ < 10−18 [42, 43]. Recently, it has been suggested that the Kerr nonlinearity can be improved to θ ≈ 10−12 with electromagnetically induced transparency (EIT) [24–27], which could be effectively used in our scheme compensated by using a strong coherent pulse. X-quadrature homodyne measurement, which is also a standard tool of continuous variable experiment, has considerably high efficiency [44]. However, during the course of considering the experiment, many factors will affect the experimental performance. Such as self-phase modulation (SPM), dispersion, molecular vibrations in Kerr media, etc. In Ref. [45], Shapiro et al. analyzed the phase noise on Kerr medium detailedly. SPM can be suppressed by operating in the slow-response regime, so phase noise is caused mainly by coupling to localized noise oscillators.

4. Conclusion

In conclusion, we have proposed a deterministic scheme for converting the four-photon GHZ state to W state by using weak cross-Kerr nonlinearities, linear optics elements, and homodyne measurement. We also investigate the effects of the quadrature homodyne measurements on the fidelity of the W state and analyze the experimental feasibility of the proposed scheme. This may be useful to future optical QIP.

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant Nos. 11264042, 11465020, 61465013, 11564041, and the Project of Jilin Science and Technology Development for Leading Talent of Science and Technology Innovation in Middle and Young and Team Project under Grant No. 20160519022JH.

References and links

1. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Opt. Express 390, 575–579 (1997).

2. J. Zhang and K. C. Peng, “Quantum teleportation and dense coding by means of bright amplitude-squeezed light and direct measurement of a Bell state,” Phys. Rev. A 62, 064302 (2000). [CrossRef]  

3. Y. S. Zhang, C. F. Li, and G. C. Guo, “Quantum key distribution via quantum encryption,” Phys. Rev. A 64, 024302 (2001). [CrossRef]  

4. X. M. Xiu, L. Dong, Y. J. Gao, and X. X. Yi, “Quantum key distribution with Einstein-Podolsky-Rosen pairs associated with weak cross-Kerr nonlinearities,” J. Opt. Soc. Am. B 29, 2869–2874 (2012). [CrossRef]  

5. F. L. Yan and T. Gao, “Quantum secret sharing between multiparty and multiparty without entanglement,” Phys. Rev. A 72, 012304 (2005). [CrossRef]  

6. H. Q. Ma, K. J. Wei, and J. H. Yang, “Experimental circular quantum secret sharing over telecom fiber network,” Opt. Express 21, 16663–16669 (2013). [CrossRef]   [PubMed]  

7. Q. Y. Cai and B. W. Li, “Improving the capacity of the Boström-Felbinger protocol,” Phys. Rev. A 69, 054301 (2004). [CrossRef]  

8. A. D. Zhu, Y. Xia, Q. B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A 73, 022338 (2006). [CrossRef]  

9. W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000). [CrossRef]  

10. A. Acín, D. Bruß, M. Lewenstein, and A. Sanpera, “Classification of Mixed Three-Qubit States,” Phys. Rev. Lett. 87, 040401 (2001). [CrossRef]   [PubMed]  

11. L. Ye and G. C. Guo, “Scheme for the generation of three-atom Greenberger-Horne-Zeilinger states and teleportation of entangled atomic states,” J. Opt. Soc. Am. B 20, 97–99 (2003). [CrossRef]  

12. A. S. Zheng, J. H. Li, R. Yu, X. Y. Lü, and Y. Wu, “Generation of Greenberger-Horne-Zeilinger state of distant diamond nitrogen-vacancy centers via nanocavity input-output process,” Opt. Express 20, 16902–16912 (2012). [CrossRef]  

13. M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999). [CrossRef]  

14. B. C. Ren and G. L. Long, “General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities,” Opt. Express 22, 6547–6561 (2014). [CrossRef]   [PubMed]  

15. N. K. Yu, C. Guo, and R. Y. Duan, “Obtaining a W state from a Greenberger-Horne-Zeilinger state via Stochastic local operations and classical communication with a rate approaching unity,” Phys. Rev. Lett. 112, 160401 (2014). [CrossRef]   [PubMed]  

16. X. Y. Lü, P. J. Song, J. B. Liu, and X. X. Yang, “N-qubit W state of spatially separated single molecule magnets,” Opt. Express 17, 14298–14311 (2009). [CrossRef]  

17. P. Walther, K. J. Resch, and A. Zeilinger, “Local conversion of Greenberger-Horne-Zeilinger states to approximate W states,” Phys. Rev. Lett. 94, 240501 (2005). [CrossRef]  

18. T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009). [CrossRef]   [PubMed]  

19. H. F. Wang, S. Zhang, A. D. Zhu, X. X. Yi, and K. H. Yeon, “Local conversion of four Einstein-Podolsky-Rosen photon pairs into four-photon polarization-entangled decoherence-free states with non-photon-number-resolving detectors,” Opt. Express 19, 25433–25440 (2011). [CrossRef]  

20. J. Song, X. D. Sun, Q. X. Mu, L. L. Zhang, Y. Xia, and H. S. Song, “Direct conversion of a four-atom W state to a Greenberger-Horne-Zeilinger state via a dissipative process,” Phys. Rev. A 88, 024305 (2013). [CrossRef]  

21. A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-Particle Entanglements from Two Entangled Pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997). [CrossRef]  

22. J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001). [CrossRef]   [PubMed]  

23. I. L. Chuang and Y. Yamamot, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995). [CrossRef]   [PubMed]  

24. W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005). [CrossRef]  

25. M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000). [CrossRef]   [PubMed]  

26. M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001). [CrossRef]  

27. S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999). [CrossRef]  

28. Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011). [CrossRef]  

29. S. L. Su, L. Zhu, Q. Guo, H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Complete Bell-state and Greenberger-Horne-Zeilinger-state nondestructive detection based on simplified symmetry analyzer,” Opt. Commun. 285, 4134–4139 (2012). [CrossRef]  

30. L. L. Sun, H. F. Wang, S. Zhang, and K. H. Yeon, “Entanglement concentration of partially entangled three-photon W states with weak cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 630–634 (2012). [CrossRef]  

31. S. L. Su, L. Y. Cheng, H. F. Wang, and S. Zhang, “An economic and feasible scheme to generate the four-photon entangled state via weak cross-Kerr nonlinearity,” Opt. Commun. 293, 172–176 (2013). [CrossRef]  

32. X. H. Li and S. Ghose, “Efficient hyperconcentration of nonlocal multipartite entanglement via the cross-Kerr nonlinearity,” Opt. Express 23, 3550–3562 (2015). [CrossRef]   [PubMed]  

33. N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985). [CrossRef]  

34. T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001). [CrossRef]  

35. M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002). [CrossRef]   [PubMed]  

36. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004). [CrossRef]  

37. T. D. Ladd, P. V. Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light,” New J. Phys. 8, 184 (2006). [CrossRef]  

38. S. J. D. Phoenix, “Wave-packet evolution in the damped oscillator,” Phys. Rev. A 41, 5132–5138 (1990). [CrossRef]   [PubMed]  

39. H. Jeong, “Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation,” Phys. Rev. A 72, 034305 (2005). [CrossRef]  

40. H. Jeong, “Quantum computation using weak nonlinearities: Robustness against decoherence,” Phys. Rev. A 73, 052320 (2006). [CrossRef]  

41. L. Dong, J. X. Wang, Q. Y. Li, H. Z. Shen, H. K. Dong, X. M. Xiu, Y. J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016). [CrossRef]  

42. R. W. Boyd, “Order-of-magnitude estimates of the nonlinear optical susceptibility,” J. Mod. Opt. 46, 367–378 (1999). [CrossRef]  

43. P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002). [CrossRef]  

44. E. S. Polzik, J. Carri, and H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992). [CrossRef]   [PubMed]  

45. J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007). [CrossRef]  

References

  • View by:

  1. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Opt. Express 390, 575–579 (1997).
  2. J. Zhang and K. C. Peng, “Quantum teleportation and dense coding by means of bright amplitude-squeezed light and direct measurement of a Bell state,” Phys. Rev. A 62, 064302 (2000).
    [Crossref]
  3. Y. S. Zhang, C. F. Li, and G. C. Guo, “Quantum key distribution via quantum encryption,” Phys. Rev. A 64, 024302 (2001).
    [Crossref]
  4. X. M. Xiu, L. Dong, Y. J. Gao, and X. X. Yi, “Quantum key distribution with Einstein-Podolsky-Rosen pairs associated with weak cross-Kerr nonlinearities,” J. Opt. Soc. Am. B 29, 2869–2874 (2012).
    [Crossref]
  5. F. L. Yan and T. Gao, “Quantum secret sharing between multiparty and multiparty without entanglement,” Phys. Rev. A 72, 012304 (2005).
    [Crossref]
  6. H. Q. Ma, K. J. Wei, and J. H. Yang, “Experimental circular quantum secret sharing over telecom fiber network,” Opt. Express 21, 16663–16669 (2013).
    [Crossref] [PubMed]
  7. Q. Y. Cai and B. W. Li, “Improving the capacity of the Boström-Felbinger protocol,” Phys. Rev. A 69, 054301 (2004).
    [Crossref]
  8. A. D. Zhu, Y. Xia, Q. B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A 73, 022338 (2006).
    [Crossref]
  9. W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
    [Crossref]
  10. A. Acín, D. Bruß, M. Lewenstein, and A. Sanpera, “Classification of Mixed Three-Qubit States,” Phys. Rev. Lett. 87, 040401 (2001).
    [Crossref] [PubMed]
  11. L. Ye and G. C. Guo, “Scheme for the generation of three-atom Greenberger-Horne-Zeilinger states and teleportation of entangled atomic states,” J. Opt. Soc. Am. B 20, 97–99 (2003).
    [Crossref]
  12. A. S. Zheng, J. H. Li, R. Yu, X. Y. Lü, and Y. Wu, “Generation of Greenberger-Horne-Zeilinger state of distant diamond nitrogen-vacancy centers via nanocavity input-output process,” Opt. Express 20, 16902–16912 (2012).
    [Crossref]
  13. M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
    [Crossref]
  14. B. C. Ren and G. L. Long, “General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities,” Opt. Express 22, 6547–6561 (2014).
    [Crossref] [PubMed]
  15. N. K. Yu, C. Guo, and R. Y. Duan, “Obtaining a W state from a Greenberger-Horne-Zeilinger state via Stochastic local operations and classical communication with a rate approaching unity,” Phys. Rev. Lett. 112, 160401 (2014).
    [Crossref] [PubMed]
  16. X. Y. Lü, P. J. Song, J. B. Liu, and X. X. Yang, “N-qubit W state of spatially separated single molecule magnets,” Opt. Express 17, 14298–14311 (2009).
    [Crossref]
  17. P. Walther, K. J. Resch, and A. Zeilinger, “Local conversion of Greenberger-Horne-Zeilinger states to approximate W states,” Phys. Rev. Lett. 94, 240501 (2005).
    [Crossref]
  18. T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
    [Crossref] [PubMed]
  19. H. F. Wang, S. Zhang, A. D. Zhu, X. X. Yi, and K. H. Yeon, “Local conversion of four Einstein-Podolsky-Rosen photon pairs into four-photon polarization-entangled decoherence-free states with non-photon-number-resolving detectors,” Opt. Express 19, 25433–25440 (2011).
    [Crossref]
  20. J. Song, X. D. Sun, Q. X. Mu, L. L. Zhang, Y. Xia, and H. S. Song, “Direct conversion of a four-atom W state to a Greenberger-Horne-Zeilinger state via a dissipative process,” Phys. Rev. A 88, 024305 (2013).
    [Crossref]
  21. A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-Particle Entanglements from Two Entangled Pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
    [Crossref]
  22. J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
    [Crossref] [PubMed]
  23. I. L. Chuang and Y. Yamamot, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995).
    [Crossref] [PubMed]
  24. W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
    [Crossref]
  25. M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
    [Crossref] [PubMed]
  26. M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001).
    [Crossref]
  27. S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
    [Crossref]
  28. Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
    [Crossref]
  29. S. L. Su, L. Zhu, Q. Guo, H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Complete Bell-state and Greenberger-Horne-Zeilinger-state nondestructive detection based on simplified symmetry analyzer,” Opt. Commun. 285, 4134–4139 (2012).
    [Crossref]
  30. L. L. Sun, H. F. Wang, S. Zhang, and K. H. Yeon, “Entanglement concentration of partially entangled three-photon W states with weak cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 630–634 (2012).
    [Crossref]
  31. S. L. Su, L. Y. Cheng, H. F. Wang, and S. Zhang, “An economic and feasible scheme to generate the four-photon entangled state via weak cross-Kerr nonlinearity,” Opt. Commun. 293, 172–176 (2013).
    [Crossref]
  32. X. H. Li and S. Ghose, “Efficient hyperconcentration of nonlocal multipartite entanglement via the cross-Kerr nonlinearity,” Opt. Express 23, 3550–3562 (2015).
    [Crossref] [PubMed]
  33. N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
    [Crossref]
  34. T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
    [Crossref]
  35. M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
    [Crossref] [PubMed]
  36. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
    [Crossref]
  37. T. D. Ladd, P. V. Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light,” New J. Phys. 8, 184 (2006).
    [Crossref]
  38. S. J. D. Phoenix, “Wave-packet evolution in the damped oscillator,” Phys. Rev. A 41, 5132–5138 (1990).
    [Crossref] [PubMed]
  39. H. Jeong, “Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation,” Phys. Rev. A 72, 034305 (2005).
    [Crossref]
  40. H. Jeong, “Quantum computation using weak nonlinearities: Robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
    [Crossref]
  41. L. Dong, J. X. Wang, Q. Y. Li, H. Z. Shen, H. K. Dong, X. M. Xiu, Y. J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
    [Crossref]
  42. R. W. Boyd, “Order-of-magnitude estimates of the nonlinear optical susceptibility,” J. Mod. Opt. 46, 367–378 (1999).
    [Crossref]
  43. P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
    [Crossref]
  44. E. S. Polzik, J. Carri, and H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
    [Crossref] [PubMed]
  45. J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
    [Crossref]

2016 (1)

L. Dong, J. X. Wang, Q. Y. Li, H. Z. Shen, H. K. Dong, X. M. Xiu, Y. J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

2015 (1)

2014 (2)

B. C. Ren and G. L. Long, “General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities,” Opt. Express 22, 6547–6561 (2014).
[Crossref] [PubMed]

N. K. Yu, C. Guo, and R. Y. Duan, “Obtaining a W state from a Greenberger-Horne-Zeilinger state via Stochastic local operations and classical communication with a rate approaching unity,” Phys. Rev. Lett. 112, 160401 (2014).
[Crossref] [PubMed]

2013 (3)

H. Q. Ma, K. J. Wei, and J. H. Yang, “Experimental circular quantum secret sharing over telecom fiber network,” Opt. Express 21, 16663–16669 (2013).
[Crossref] [PubMed]

J. Song, X. D. Sun, Q. X. Mu, L. L. Zhang, Y. Xia, and H. S. Song, “Direct conversion of a four-atom W state to a Greenberger-Horne-Zeilinger state via a dissipative process,” Phys. Rev. A 88, 024305 (2013).
[Crossref]

S. L. Su, L. Y. Cheng, H. F. Wang, and S. Zhang, “An economic and feasible scheme to generate the four-photon entangled state via weak cross-Kerr nonlinearity,” Opt. Commun. 293, 172–176 (2013).
[Crossref]

2012 (4)

2011 (2)

2009 (2)

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[Crossref] [PubMed]

X. Y. Lü, P. J. Song, J. B. Liu, and X. X. Yang, “N-qubit W state of spatially separated single molecule magnets,” Opt. Express 17, 14298–14311 (2009).
[Crossref]

2007 (1)

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[Crossref]

2006 (3)

T. D. Ladd, P. V. Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light,” New J. Phys. 8, 184 (2006).
[Crossref]

H. Jeong, “Quantum computation using weak nonlinearities: Robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
[Crossref]

A. D. Zhu, Y. Xia, Q. B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A 73, 022338 (2006).
[Crossref]

2005 (4)

F. L. Yan and T. Gao, “Quantum secret sharing between multiparty and multiparty without entanglement,” Phys. Rev. A 72, 012304 (2005).
[Crossref]

P. Walther, K. J. Resch, and A. Zeilinger, “Local conversion of Greenberger-Horne-Zeilinger states to approximate W states,” Phys. Rev. Lett. 94, 240501 (2005).
[Crossref]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

H. Jeong, “Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation,” Phys. Rev. A 72, 034305 (2005).
[Crossref]

2004 (2)

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[Crossref]

Q. Y. Cai and B. W. Li, “Improving the capacity of the Boström-Felbinger protocol,” Phys. Rev. A 69, 054301 (2004).
[Crossref]

2003 (1)

2002 (2)

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
[Crossref] [PubMed]

P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[Crossref]

2001 (5)

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[Crossref]

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001).
[Crossref]

Y. S. Zhang, C. F. Li, and G. C. Guo, “Quantum key distribution via quantum encryption,” Phys. Rev. A 64, 024302 (2001).
[Crossref]

A. Acín, D. Bruß, M. Lewenstein, and A. Sanpera, “Classification of Mixed Three-Qubit States,” Phys. Rev. Lett. 87, 040401 (2001).
[Crossref] [PubMed]

2000 (3)

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[Crossref]

J. Zhang and K. C. Peng, “Quantum teleportation and dense coding by means of bright amplitude-squeezed light and direct measurement of a Bell state,” Phys. Rev. A 62, 064302 (2000).
[Crossref]

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[Crossref] [PubMed]

1999 (3)

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[Crossref]

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

R. W. Boyd, “Order-of-magnitude estimates of the nonlinear optical susceptibility,” J. Mod. Opt. 46, 367–378 (1999).
[Crossref]

1997 (2)

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Opt. Express 390, 575–579 (1997).

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-Particle Entanglements from Two Entangled Pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[Crossref]

1995 (1)

I. L. Chuang and Y. Yamamot, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995).
[Crossref] [PubMed]

1992 (1)

E. S. Polzik, J. Carri, and H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
[Crossref] [PubMed]

1990 (1)

S. J. D. Phoenix, “Wave-packet evolution in the damped oscillator,” Phys. Rev. A 41, 5132–5138 (1990).
[Crossref] [PubMed]

1985 (1)

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[Crossref]

Acín, A.

A. Acín, D. Bruß, M. Lewenstein, and A. Sanpera, “Classification of Mixed Three-Qubit States,” Phys. Rev. Lett. 87, 040401 (2001).
[Crossref] [PubMed]

Armen, M. A.

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
[Crossref] [PubMed]

Au, J. K.

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
[Crossref] [PubMed]

Bai, J.

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[Crossref]

Beausoleil, R. G.

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

Berthiaume, A.

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

Bouwmeester, D.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Opt. Express 390, 575–579 (1997).

Boyd, R. W.

R. W. Boyd, “Order-of-magnitude estimates of the nonlinear optical susceptibility,” J. Mod. Opt. 46, 367–378 (1999).
[Crossref]

Bruß, D.

A. Acín, D. Bruß, M. Lewenstein, and A. Sanpera, “Classification of Mixed Three-Qubit States,” Phys. Rev. Lett. 87, 040401 (2001).
[Crossref] [PubMed]

Bužek, V.

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

Cai, Q. Y.

Q. Y. Cai and B. W. Li, “Improving the capacity of the Boström-Felbinger protocol,” Phys. Rev. A 69, 054301 (2004).
[Crossref]

Carri, J.

E. S. Polzik, J. Carri, and H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
[Crossref] [PubMed]

Cheng, L. Y.

S. L. Su, L. Y. Cheng, H. F. Wang, and S. Zhang, “An economic and feasible scheme to generate the four-photon entangled state via weak cross-Kerr nonlinearity,” Opt. Commun. 293, 172–176 (2013).
[Crossref]

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[Crossref]

Chuang, I. L.

I. L. Chuang and Y. Yamamot, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995).
[Crossref] [PubMed]

Cirac, J. I.

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[Crossref]

Daniell, M.

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

Doherty, A. C.

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
[Crossref] [PubMed]

Dong, H. K.

L. Dong, J. X. Wang, Q. Y. Li, H. Z. Shen, H. K. Dong, X. M. Xiu, Y. J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

Dong, L.

L. Dong, J. X. Wang, Q. Y. Li, H. Z. Shen, H. K. Dong, X. M. Xiu, Y. J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

X. M. Xiu, L. Dong, Y. J. Gao, and X. X. Yi, “Quantum key distribution with Einstein-Podolsky-Rosen pairs associated with weak cross-Kerr nonlinearities,” J. Opt. Soc. Am. B 29, 2869–2874 (2012).
[Crossref]

Dowling, J. P.

P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[Crossref]

Duan, R. Y.

N. K. Yu, C. Guo, and R. Y. Duan, “Obtaining a W state from a Greenberger-Horne-Zeilinger state via Stochastic local operations and classical communication with a rate approaching unity,” Phys. Rev. Lett. 112, 160401 (2014).
[Crossref] [PubMed]

Dür, W.

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[Crossref]

Eibl, M.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Opt. Express 390, 575–579 (1997).

Fan, Q. B.

A. D. Zhu, Y. Xia, Q. B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A 73, 022338 (2006).
[Crossref]

Franson, J. D.

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[Crossref]

Gao, T.

F. L. Yan and T. Gao, “Quantum secret sharing between multiparty and multiparty without entanglement,” Phys. Rev. A 72, 012304 (2005).
[Crossref]

Gao, Y. J.

L. Dong, J. X. Wang, Q. Y. Li, H. Z. Shen, H. K. Dong, X. M. Xiu, Y. J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

X. M. Xiu, L. Dong, Y. J. Gao, and X. X. Yi, “Quantum key distribution with Einstein-Podolsky-Rosen pairs associated with weak cross-Kerr nonlinearities,” J. Opt. Soc. Am. B 29, 2869–2874 (2012).
[Crossref]

Gasparoni, S.

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

Ghose, S.

Guo, C.

N. K. Yu, C. Guo, and R. Y. Duan, “Obtaining a W state from a Greenberger-Horne-Zeilinger state via Stochastic local operations and classical communication with a rate approaching unity,” Phys. Rev. Lett. 112, 160401 (2014).
[Crossref] [PubMed]

Guo, G. C.

Guo, Q.

S. L. Su, L. Zhu, Q. Guo, H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Complete Bell-state and Greenberger-Horne-Zeilinger-state nondestructive detection based on simplified symmetry analyzer,” Opt. Commun. 285, 4134–4139 (2012).
[Crossref]

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[Crossref]

Harris, S. E.

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[Crossref]

Hau, L. V.

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[Crossref]

Haus, H. A.

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[Crossref]

Hillery, M.

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

Horne, M. A.

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-Particle Entanglements from Two Entangled Pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[Crossref]

Imamoglu, A.

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001).
[Crossref]

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[Crossref] [PubMed]

Imoto, N.

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[Crossref] [PubMed]

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[Crossref]

Jacobs, B. C.

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[Crossref]

Jeong, H.

H. Jeong, “Quantum computation using weak nonlinearities: Robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
[Crossref]

H. Jeong, “Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation,” Phys. Rev. A 72, 034305 (2005).
[Crossref]

Kimble, H. J.

E. S. Polzik, J. Carri, and H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
[Crossref] [PubMed]

Koashi, M.

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[Crossref] [PubMed]

Kok, P.

P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[Crossref]

Ladd, T. D.

T. D. Ladd, P. V. Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light,” New J. Phys. 8, 184 (2006).
[Crossref]

Lee, H.

P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[Crossref]

Lewenstein, M.

A. Acín, D. Bruß, M. Lewenstein, and A. Sanpera, “Classification of Mixed Three-Qubit States,” Phys. Rev. Lett. 87, 040401 (2001).
[Crossref] [PubMed]

Li, B. W.

Q. Y. Cai and B. W. Li, “Improving the capacity of the Boström-Felbinger protocol,” Phys. Rev. A 69, 054301 (2004).
[Crossref]

Li, C. F.

Y. S. Zhang, C. F. Li, and G. C. Guo, “Quantum key distribution via quantum encryption,” Phys. Rev. A 64, 024302 (2001).
[Crossref]

Li, J. H.

Li, Q. Y.

L. Dong, J. X. Wang, Q. Y. Li, H. Z. Shen, H. K. Dong, X. M. Xiu, Y. J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

Li, X. H.

Liu, J. B.

Long, G. L.

Loock, P. V.

T. D. Ladd, P. V. Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light,” New J. Phys. 8, 184 (2006).
[Crossref]

Lü, X. Y.

Lukin, M. D.

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001).
[Crossref]

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[Crossref] [PubMed]

Ma, H. Q.

Mabuchi, H.

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
[Crossref] [PubMed]

Mattle, K.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Opt. Express 390, 575–579 (1997).

Mu, Q. X.

J. Song, X. D. Sun, Q. X. Mu, L. L. Zhang, Y. Xia, and H. S. Song, “Direct conversion of a four-atom W state to a Greenberger-Horne-Zeilinger state via a dissipative process,” Phys. Rev. A 88, 024305 (2013).
[Crossref]

Munro, W. J.

T. D. Ladd, P. V. Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light,” New J. Phys. 8, 184 (2006).
[Crossref]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[Crossref]

Nemoto, K.

T. D. Ladd, P. V. Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light,” New J. Phys. 8, 184 (2006).
[Crossref]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[Crossref]

Oh, C. H.

L. Dong, J. X. Wang, Q. Y. Li, H. Z. Shen, H. K. Dong, X. M. Xiu, Y. J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

Özdemir, S. K.

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[Crossref] [PubMed]

Pan, J. W.

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Opt. Express 390, 575–579 (1997).

Peng, K. C.

J. Zhang and K. C. Peng, “Quantum teleportation and dense coding by means of bright amplitude-squeezed light and direct measurement of a Bell state,” Phys. Rev. A 62, 064302 (2000).
[Crossref]

Phoenix, S. J. D.

S. J. D. Phoenix, “Wave-packet evolution in the damped oscillator,” Phys. Rev. A 41, 5132–5138 (1990).
[Crossref] [PubMed]

Pittman, T. B.

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[Crossref]

Polzik, E. S.

E. S. Polzik, J. Carri, and H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
[Crossref] [PubMed]

Razavi, M.

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[Crossref]

Ren, B. C.

Resch, K. J.

P. Walther, K. J. Resch, and A. Zeilinger, “Local conversion of Greenberger-Horne-Zeilinger states to approximate W states,” Phys. Rev. Lett. 94, 240501 (2005).
[Crossref]

Sanpera, A.

A. Acín, D. Bruß, M. Lewenstein, and A. Sanpera, “Classification of Mixed Three-Qubit States,” Phys. Rev. Lett. 87, 040401 (2001).
[Crossref] [PubMed]

Shao, X. Q.

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[Crossref]

Shapiro, J. H.

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[Crossref]

Shen, H. Z.

L. Dong, J. X. Wang, Q. Y. Li, H. Z. Shen, H. K. Dong, X. M. Xiu, Y. J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

Song, H. S.

J. Song, X. D. Sun, Q. X. Mu, L. L. Zhang, Y. Xia, and H. S. Song, “Direct conversion of a four-atom W state to a Greenberger-Horne-Zeilinger state via a dissipative process,” Phys. Rev. A 88, 024305 (2013).
[Crossref]

Song, J.

J. Song, X. D. Sun, Q. X. Mu, L. L. Zhang, Y. Xia, and H. S. Song, “Direct conversion of a four-atom W state to a Greenberger-Horne-Zeilinger state via a dissipative process,” Phys. Rev. A 88, 024305 (2013).
[Crossref]

Song, P. J.

Spiller, T. P.

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

Stockton, J. K.

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
[Crossref] [PubMed]

Su, S. L.

S. L. Su, L. Y. Cheng, H. F. Wang, and S. Zhang, “An economic and feasible scheme to generate the four-photon entangled state via weak cross-Kerr nonlinearity,” Opt. Commun. 293, 172–176 (2013).
[Crossref]

S. L. Su, L. Zhu, Q. Guo, H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Complete Bell-state and Greenberger-Horne-Zeilinger-state nondestructive detection based on simplified symmetry analyzer,” Opt. Commun. 285, 4134–4139 (2012).
[Crossref]

Sun, L. L.

Sun, X. D.

J. Song, X. D. Sun, Q. X. Mu, L. L. Zhang, Y. Xia, and H. S. Song, “Direct conversion of a four-atom W state to a Greenberger-Horne-Zeilinger state via a dissipative process,” Phys. Rev. A 88, 024305 (2013).
[Crossref]

Tashima, T.

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[Crossref] [PubMed]

Vidal, G.

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[Crossref]

Wakatsuki, T.

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[Crossref] [PubMed]

Walther, P.

P. Walther, K. J. Resch, and A. Zeilinger, “Local conversion of Greenberger-Horne-Zeilinger states to approximate W states,” Phys. Rev. Lett. 94, 240501 (2005).
[Crossref]

Wang, H. F.

S. L. Su, L. Y. Cheng, H. F. Wang, and S. Zhang, “An economic and feasible scheme to generate the four-photon entangled state via weak cross-Kerr nonlinearity,” Opt. Commun. 293, 172–176 (2013).
[Crossref]

L. L. Sun, H. F. Wang, S. Zhang, and K. H. Yeon, “Entanglement concentration of partially entangled three-photon W states with weak cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 630–634 (2012).
[Crossref]

S. L. Su, L. Zhu, Q. Guo, H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Complete Bell-state and Greenberger-Horne-Zeilinger-state nondestructive detection based on simplified symmetry analyzer,” Opt. Commun. 285, 4134–4139 (2012).
[Crossref]

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[Crossref]

H. F. Wang, S. Zhang, A. D. Zhu, X. X. Yi, and K. H. Yeon, “Local conversion of four Einstein-Podolsky-Rosen photon pairs into four-photon polarization-entangled decoherence-free states with non-photon-number-resolving detectors,” Opt. Express 19, 25433–25440 (2011).
[Crossref]

Wang, J. X.

L. Dong, J. X. Wang, Q. Y. Li, H. Z. Shen, H. K. Dong, X. M. Xiu, Y. J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

Wei, K. J.

Weihs, G.

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

Weinfurter, H.

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-Particle Entanglements from Two Entangled Pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[Crossref]

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Opt. Express 390, 575–579 (1997).

Wu, Y.

Xia, Y.

J. Song, X. D. Sun, Q. X. Mu, L. L. Zhang, Y. Xia, and H. S. Song, “Direct conversion of a four-atom W state to a Greenberger-Horne-Zeilinger state via a dissipative process,” Phys. Rev. A 88, 024305 (2013).
[Crossref]

A. D. Zhu, Y. Xia, Q. B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A 73, 022338 (2006).
[Crossref]

Xiu, X. M.

L. Dong, J. X. Wang, Q. Y. Li, H. Z. Shen, H. K. Dong, X. M. Xiu, Y. J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

X. M. Xiu, L. Dong, Y. J. Gao, and X. X. Yi, “Quantum key distribution with Einstein-Podolsky-Rosen pairs associated with weak cross-Kerr nonlinearities,” J. Opt. Soc. Am. B 29, 2869–2874 (2012).
[Crossref]

Yamamot, Y.

I. L. Chuang and Y. Yamamot, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995).
[Crossref] [PubMed]

Yamamoto, T.

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[Crossref] [PubMed]

Yamamoto, Y.

T. D. Ladd, P. V. Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light,” New J. Phys. 8, 184 (2006).
[Crossref]

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[Crossref]

Yan, F. L.

F. L. Yan and T. Gao, “Quantum secret sharing between multiparty and multiparty without entanglement,” Phys. Rev. A 72, 012304 (2005).
[Crossref]

Yang, J. H.

Yang, X. X.

Ye, L.

Yeon, K. H.

Yi, X. X.

Yu, N. K.

N. K. Yu, C. Guo, and R. Y. Duan, “Obtaining a W state from a Greenberger-Horne-Zeilinger state via Stochastic local operations and classical communication with a rate approaching unity,” Phys. Rev. Lett. 112, 160401 (2014).
[Crossref] [PubMed]

Yu, R.

Zeilinger, A.

P. Walther, K. J. Resch, and A. Zeilinger, “Local conversion of Greenberger-Horne-Zeilinger states to approximate W states,” Phys. Rev. Lett. 94, 240501 (2005).
[Crossref]

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-Particle Entanglements from Two Entangled Pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[Crossref]

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Opt. Express 390, 575–579 (1997).

Zhang, J.

J. Zhang and K. C. Peng, “Quantum teleportation and dense coding by means of bright amplitude-squeezed light and direct measurement of a Bell state,” Phys. Rev. A 62, 064302 (2000).
[Crossref]

Zhang, L. L.

J. Song, X. D. Sun, Q. X. Mu, L. L. Zhang, Y. Xia, and H. S. Song, “Direct conversion of a four-atom W state to a Greenberger-Horne-Zeilinger state via a dissipative process,” Phys. Rev. A 88, 024305 (2013).
[Crossref]

Zhang, S.

S. L. Su, L. Y. Cheng, H. F. Wang, and S. Zhang, “An economic and feasible scheme to generate the four-photon entangled state via weak cross-Kerr nonlinearity,” Opt. Commun. 293, 172–176 (2013).
[Crossref]

L. L. Sun, H. F. Wang, S. Zhang, and K. H. Yeon, “Entanglement concentration of partially entangled three-photon W states with weak cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 630–634 (2012).
[Crossref]

S. L. Su, L. Zhu, Q. Guo, H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Complete Bell-state and Greenberger-Horne-Zeilinger-state nondestructive detection based on simplified symmetry analyzer,” Opt. Commun. 285, 4134–4139 (2012).
[Crossref]

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[Crossref]

H. F. Wang, S. Zhang, A. D. Zhu, X. X. Yi, and K. H. Yeon, “Local conversion of four Einstein-Podolsky-Rosen photon pairs into four-photon polarization-entangled decoherence-free states with non-photon-number-resolving detectors,” Opt. Express 19, 25433–25440 (2011).
[Crossref]

A. D. Zhu, Y. Xia, Q. B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A 73, 022338 (2006).
[Crossref]

Zhang, Y. S.

Y. S. Zhang, C. F. Li, and G. C. Guo, “Quantum key distribution via quantum encryption,” Phys. Rev. A 64, 024302 (2001).
[Crossref]

Zheng, A. S.

Zhu, A. D.

S. L. Su, L. Zhu, Q. Guo, H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Complete Bell-state and Greenberger-Horne-Zeilinger-state nondestructive detection based on simplified symmetry analyzer,” Opt. Commun. 285, 4134–4139 (2012).
[Crossref]

H. F. Wang, S. Zhang, A. D. Zhu, X. X. Yi, and K. H. Yeon, “Local conversion of four Einstein-Podolsky-Rosen photon pairs into four-photon polarization-entangled decoherence-free states with non-photon-number-resolving detectors,” Opt. Express 19, 25433–25440 (2011).
[Crossref]

A. D. Zhu, Y. Xia, Q. B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A 73, 022338 (2006).
[Crossref]

Zhu, L.

S. L. Su, L. Zhu, Q. Guo, H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Complete Bell-state and Greenberger-Horne-Zeilinger-state nondestructive detection based on simplified symmetry analyzer,” Opt. Commun. 285, 4134–4139 (2012).
[Crossref]

Zukowski, M.

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-Particle Entanglements from Two Entangled Pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[Crossref]

J. Mod. Opt. (1)

R. W. Boyd, “Order-of-magnitude estimates of the nonlinear optical susceptibility,” J. Mod. Opt. 46, 367–378 (1999).
[Crossref]

J. Opt. Soc. Am. B (3)

Nature (London) (1)

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001).
[Crossref]

New J. Phys. (2)

T. D. Ladd, P. V. Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light,” New J. Phys. 8, 184 (2006).
[Crossref]

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[Crossref]

Opt. Commun. (2)

S. L. Su, L. Y. Cheng, H. F. Wang, and S. Zhang, “An economic and feasible scheme to generate the four-photon entangled state via weak cross-Kerr nonlinearity,” Opt. Commun. 293, 172–176 (2013).
[Crossref]

S. L. Su, L. Zhu, Q. Guo, H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Complete Bell-state and Greenberger-Horne-Zeilinger-state nondestructive detection based on simplified symmetry analyzer,” Opt. Commun. 285, 4134–4139 (2012).
[Crossref]

Opt. Express (7)

Phys. Rev. A (18)

Q. Y. Cai and B. W. Li, “Improving the capacity of the Boström-Felbinger protocol,” Phys. Rev. A 69, 054301 (2004).
[Crossref]

A. D. Zhu, Y. Xia, Q. B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A 73, 022338 (2006).
[Crossref]

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[Crossref]

J. Zhang and K. C. Peng, “Quantum teleportation and dense coding by means of bright amplitude-squeezed light and direct measurement of a Bell state,” Phys. Rev. A 62, 064302 (2000).
[Crossref]

Y. S. Zhang, C. F. Li, and G. C. Guo, “Quantum key distribution via quantum encryption,” Phys. Rev. A 64, 024302 (2001).
[Crossref]

F. L. Yan and T. Gao, “Quantum secret sharing between multiparty and multiparty without entanglement,” Phys. Rev. A 72, 012304 (2005).
[Crossref]

J. Song, X. D. Sun, Q. X. Mu, L. L. Zhang, Y. Xia, and H. S. Song, “Direct conversion of a four-atom W state to a Greenberger-Horne-Zeilinger state via a dissipative process,” Phys. Rev. A 88, 024305 (2013).
[Crossref]

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[Crossref]

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[Crossref]

S. J. D. Phoenix, “Wave-packet evolution in the damped oscillator,” Phys. Rev. A 41, 5132–5138 (1990).
[Crossref] [PubMed]

H. Jeong, “Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation,” Phys. Rev. A 72, 034305 (2005).
[Crossref]

H. Jeong, “Quantum computation using weak nonlinearities: Robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
[Crossref]

L. Dong, J. X. Wang, Q. Y. Li, H. Z. Shen, H. K. Dong, X. M. Xiu, Y. J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

I. L. Chuang and Y. Yamamot, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995).
[Crossref] [PubMed]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[Crossref]

P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[Crossref]

Phys. Rev. Lett. (11)

E. S. Polzik, J. Carri, and H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
[Crossref] [PubMed]

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[Crossref]

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[Crossref] [PubMed]

P. Walther, K. J. Resch, and A. Zeilinger, “Local conversion of Greenberger-Horne-Zeilinger states to approximate W states,” Phys. Rev. Lett. 94, 240501 (2005).
[Crossref]

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[Crossref] [PubMed]

M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002).
[Crossref] [PubMed]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[Crossref]

N. K. Yu, C. Guo, and R. Y. Duan, “Obtaining a W state from a Greenberger-Horne-Zeilinger state via Stochastic local operations and classical communication with a rate approaching unity,” Phys. Rev. Lett. 112, 160401 (2014).
[Crossref] [PubMed]

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-Particle Entanglements from Two Entangled Pairs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[Crossref]

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

A. Acín, D. Bruß, M. Lewenstein, and A. Sanpera, “Classification of Mixed Three-Qubit States,” Phys. Rev. Lett. 87, 040401 (2001).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 Cross-Kerr nonlinear interaction model.
Fig. 2
Fig. 2 Schematic diagram for conversion from a GHZ state to a W state. And the qubit flip (QF) device is composed of two HV-PBS and a phase shifter (PS). Here, the FS-PBS, which transmits F-polarized photons and reflects S-polarized photons is the polarizing beam splitter (PBS) in the |F〉 and |S〉 basis. HV-PBS, which transmits H-polarized photons and reflects V-polarized photons, is the PBS in the in the |H〉 and |V〉 basis. PS denotes a phase shifter, which is to realize the transformation: |H〉 → |H〉, |V〉 → −|V〉.
Fig. 3
Fig. 3 (a) The effects of the homodyne measurement on the fidelity of the W state versus the amplitude of coherent state α and the distance between the measurement results and the phase shift angle θ, here we set δ = 10. (b) The effects of the homodyne measurement on the fidelity of the W state versus the amplitude of coherent state α and the distance between the measurement results and the peak δ, here we set θ = 0.01. (c) The effects of the homodyne measurement on the fidelity of the W state versus the phase shift angle θ and the distance between the measurement results and the peak δ, here we set α = 40000.
Fig. 4
Fig. 4 Curves of the homodyne measurement result X with α = 40000 and θ = 0.01.
Fig. 5
Fig. 5 (a) The measurement error rate versus the decoherence coefficient A and the amplitude α of the coherent state, here we set θ = 0.01. (b) The fidelity of the output state versus the decoherence coefficient A and the amplitude α of the coherent state, where we set the δ = 0.1d1, θ = 0.01.

Equations (13)

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H ^ QND = h ¯ χ a ^ s a ^ s a ^ p a ^ p .
U ck | Φ | α = e i H ^ QND t / h ¯ ( a | 0 + b | 1 ) | α = a | 0 | α + b | 1 | α e i θ .
| ϕ 0 = 1 2 ( | H 1 | H 2 | H 3 | H 4 + | V 1 | V 2 | V 3 | V 4 ) .
| ϕ 0 = 1 2 2 ( | F 1 | F 2 | F 3 | F 4 + | F 1 | S 2 | F 3 | S 4 + | S 1 | F 2 | F 3 | S 4 + | S 1 | S 2 | F 3 | F 4 + | F 1 | F 2 | S 3 | S 4 + | F 1 | S 2 | S 3 | F 4 + | S 1 | F 2 | S 3 | F 4 + | S 1 | S 2 | S 3 | S 4 ) | α .
| ϕ 2 = 1 2 2 [ ( | S a | F b | F c | F d + | F a | S b | F c | S d + | S a | F b | S c | S d + | F a | F b | F c | S d ) + | α e 3 θ + ( | F a | S b | S c | S d + | S a | F b | F c | F d + | S a | S b | F c | S d + | S a | S b | S c | F d ) | α e θ ] .
| ϕ X X | ϕ 3 = 1 N [ 2 f ( x , α cos 3 θ ) e i ϕ ( X ) 1 | φ 1 + 2 f ( x , α cos θ ) e i φ ( X ) 2 | φ 2 ] ,
f ( x , β ) = exp [ 1 4 ( x 2 β ) 2 ] / ( 2 π ) 1 / 4 , ϕ ( X ) 1 = α sin 3 θ ( x 2 α cos 3 θ ) Mod 2 π , ϕ ( X ) 2 = α sin θ ( x 2 α cos θ ) Mod 2 π , | φ 1 = 1 2 ( | S a | F b | F c | F d + | F a | S b | F c | S d + | F a | F b | S c | F d + | F a | F b | F c | S d ) , | φ 2 = 1 2 ( | F a | S b | S c | S d + | S a | F b | S c | S d + | S a | S b | F c | S d + | S a | S b | S c | F d ) , N [ 4 f 2 ( x , α cos 3 θ ) + 4 f 2 ( x , α cos θ ) ] 1 / 2 .
F ( X 1 ) = | φ | ϕ 1 X | 1 1 + e 2 d 1 ( d 1 δ 1 ) ,
ρ t = J ^ ρ + L ^ ρ , J ^ ρ = γ a ρ a , L ^ ρ = γ 2 ( a a ρ + ρ a a ) .
ρ ( t ) = [ D ˜ ( Δ t ) U ˜ ( Δ t ) ] N ρ ( 0 ) = j , k = 1 , 3 e B j , k ( | ϕ j ϕ k | ) | A a e i j θ A a e i k θ | ,
A = γ t / 2 , B j , k = α 2 ( 1 A 2 N ) n = 1 N A 2 ( n 1 ) N [ e i ( J k ) n θ N 1 ] .
| x ρ ( t ) x | = j , k = 1 , 3 C j , k ( | ϕ j ϕ k | ) f ( x , j θ ) f ( x , k θ ) e i [ μ j k + φ ( x , j θ ) φ ( x , k θ ) ] ,
C j , k = e Re ( B j k ) , μ j k = Im ( B j k ) , f ( x , n θ ) = exp [ 1 4 ( x 2 A α cos n θ ) 2 ) ] / ( 2 π ) 1 / 4 ( n = 1 , 3 ) , φ ( x , n θ ) = ( x 2 A α cos n θ ) A α sin n θ ( n = 1 , 3 ) .

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