Abstract

We theoretically investigate an entanglement purification protocol with photon and electron hybrid entangled state resorting to quantum-dot spin and microcavity coupled system. The present system is used to construct the parity check gate which allows a quantum nonde-molition measurement on the spin parity. The cavity-spin coupled system provides a novel experimental platform of quantum information processing with photon and solid qubit.

© 2011 OSA

1. Introduction

In recent years, there has been substantial interest in quantum information processing (QIP) based on quantum entanglement. The unique properties of quantum entanglement have many applications, such as quantum cryptography [1, 2], quantum dense coding [3], quantum teleportation [4], quantum repeaters [57] and quantum direction communication [8, 9]. However, pure entanglement is difficult to achieve in practice because of the environment noise which will decrease the entanglement of particles and reduce the success probability of QIP. Entanglement purification is used to solve this problem by which maximally entangled states can be obtained from an ensemble in a mixed entangled state. The first entanglement purification protocol (EPP) was proposed by Bennett et al. [10] in which Werner states can be purified by using controlled not (CNOT) gates and bilateral rotations. Later, EPP was improved by Deutsch et al. for quantum privacy amplification process using similar logic operations [11]. In 1998, Briegel et al. present an novel way for long distance quantum communication using quantum repeaters based on entanglement purification and entanglement swapping [12]. Thus, EPP becomes an important element in long-distance quantum communication and had been widely investigated. Pan et al. [13] introduced an EPP model resorting to polarization beam splitters (PBSs) and single photon detectors in 2001. The experimental demonstration of EPP based on linear optics was accomplished in 2003 [14]. EPP based on the parametric down-conversion (PDC) source was presented by Simon and Pan in 2002 [15] which exploits spatial entanglement to purify the entanglement in polarization degrees of freedom. Sheng et al. also proposed an EPP based on PDC source using quantum nondemolition detectors [16]. In 2008, Xiao et al. [17] proposed an EPP with frequency and polarization hyper-entanglement. In the past decades, EPP has widely been studied and there are many related research works [1823].

Recently, there is a novel system for QIP based on a charged quantum-dot (QD) carrying a single spin coupled to an optical microcavity [2427]. The device exploits the photon-spin entangling gate that can be achieved in this system. Auffèves-Garnier et al. presented that the neutral QD-cavity system behaves like a beam splitter in the limit of weak incoming field [28]. Hybrid entanglement is considered to be an useful resource in realizing QIP and there are various research on hybrid quantum entanglement. In 2006, quantum repeaters based on hybrid entangled states have been experimentally realized [29]. Later, Azuma et al. proposed a realistic protocol to generate entanglement between quantum memories at neighboring nodes in hybrid quantum repeaters [30]. In 2009, Waks and Monroe present a scheme of creating hybrid entanglement between semiconductor and atomic quantum systems [31]. Brask et al. proposed a hybrid quantum repeater protocol for long-distance entanglement distribution [32]. The hybrid entangled state shows entanglement in different degrees of freedom and provides a new way of QIP. In Ref. [26], they proposed an efficient way of hybrid entanglement generation using QD and microcavity coupled system in which entanglement can be realized between photon polarization and electron spins. The QD and cavity coupled system provides a novel way of building blocks required for solid-state quantum networks, such as quantum memories, entanglement swapping and quantum teleportation [27], and various quantum logic gates [33].

Motivated by the observation of reflection spectroscopy in QD and microcavity coupled system [34] and their possible use for circuit QED system, we presented an entanglement purification protocol for photon-spin hybrid entangled state exploiting the QD and microcavity coupled system. In this scheme, ancillary photon and cavity system play the role of a parity check on the spins. In our proposed protocol, both the big-flip errors and phase-flip errors can be corrected by photon and electron interaction and the fidelity of entanglement can be increased. The proposed setup can easily be realized using current technology.

This paper is organized as follows. In Sec. 2, we introduce our parity check gate model and proposed the hybrid entanglement purification protocol. In Sec. 3, we discuss the efficiency and errors on a practical implementation. Finally, in Sec. 4, we summarize our results and discus future prospects.

2. Theoretical model of hybrid entanglement purification using QD and micro-cavity coupled system

We propose to purify the noise errors of photon and electron spin hybrid entangled state using QD and microcavity coupled system. The system is composed of a singly charged QD in micropillar microcavities. Figure 1 shows a schematic of our model. The optical properties of singly charged QDs are dominated by the optical transitions of the negatively charged exciton X that consists of two electrons bound to one hole. As illustrated by Pauli’s exclusion principle, the exciton can be created by the optical excitation of the system, e.g., when a photon passes through the cavity and interacts with the electron in the coupling cavity, the left circularly polarized photon only couples with the cavity when the electron in the spin up state |↑〉 and generate the exciton X in the state |↑↓⇑〉; the right circularly polarized photon only couples with the cavity when the electron of spin is in the spin down state |↓〉 and generate the exciton in the state |↓↑⇓〉. Here |⇑〉 and |⇓〉 represent the spin direction of the heavy hole spin state.

 

Fig. 1 Schematic of QD and microcavity coupled system. The diagram shows the principle of hybrid entanglement generation in quantum dot and cavity coupled system.

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The Heisenberg equations of motion describing the dynamics of the cavity field operator â and the trion X dipole operator σ can be written as [25, 35]

da^dt=[i(ωCω)+κ+κs2]a^gσκa^inκa^in+H^
dσdt=[i(ωXω)+γ2]σgσza^+G^
where g represents the coupling constant, γ2 is the excition dipole decay rate. κs and κ are the cavity decay rate and the leaky rate, respectively. Ĥ and Ĝ are the noise operators related to reservoirs. And we denote the frequencies of the input photon, cavity mode and the spin-dependent optical transition by ω, ωC, ωX, respectively.

In addition to Eqs. (1) and (2), we have the following relation between the incoming and outgoing field operators [25, 35]

a^r=a^in+κa^a^t=a^in+κa^
here âin and âin are the input field operators from different side of the cavity, âr and ât are the reflected and transmitted operators, respectively.

The reflection and transmission coefficients of this microcavity system can be investigated by solving the Heisenberg equations of motion for the cavity field operator and the trion dipole operator as discussed in Ref. [25] which can be described by

r(ω)=[i(ωXω)+γ2][i(ωcω)+κs2]+g2[i(ωXω)+γ2][i(ωcω)+κ+κs2]+g2t(ω)=κ[i(ωXω)+γ2][i(ωXω)+γ2][i(ωcω)+κ+κs2]+g2.
On condition that the resonant interaction with ωc = ωX = ω0, by taking g = 0, the the reflection and transmission coefficients r and t for the uncoupled cavity system can be written as
r0(ω)=i(ω0ω)+κs2i(ω0ω)+κs2+κt0(ω)=κi(ω0ω)+κs2+κ.
For example, the spin of QD in microcavity is in the up direction with s=1/2, if a photon in the left circular polarized state is passed through the cavity, it couples with the cavity and the exciton can be generated. Thus the reflected coefficient and transmitted coefficient are described by |r(ω)| and |t(ω)|, respectively. However, the right circular polarized photon will not couple with the cavity as the right circular polarized photon only couple the cavity with the spin of QD in the down direction (s=−1/2), the reflected coefficient and transmitted coefficient are described by |r0(ω)| and |t0(ω)|, respectively. So the left circular polarized photon feels a coupled cavity, the reflection coefficient in Eq. (4) is equal to unity. The right circular polarized photon feels an uncoupled cavity with the coupling constant g=0, the transmission coefficient in Eq. (5) is equal to 1. This process has been developed in the quantum information processes, such as entanglement generation [24], CNot operation and Bell state analysis [26], entanglement swapping [27] and so on.

It becomes clear from the discussion above that the dynamics of photon and electron interaction in QD and microcavity coupled system can be described by the follow equations:

|R,|L,,|L,|L,,|R,|R,,|L,|R,,|R,|R,,|L,|R,,|R,|L,,|L,|L,,
here |L〉 and |R〉 represent the state of the left and right circular polarized photons, respectively. The superscript arrow in the photon state indicates the propagation direction along the z axis and the arrows represent the direction of the electrons. When a circularly polarized photon passes through the cavity and interacts with QD, the photon will either be transmitted or be reflected by the cavity according to the spin direction of the QD, e.g., a right circularly polarized photon passes through the cavity with QD in spin up state, the photon will be reflected by the cavity and the polarized state of the photon and the direction of propagation will both changed. Thus the photon polarization and electron spin may get entangled if the initial electron state is superposed. The principles of photon and electron entangler is shown in Fig. 1. The entangler works as follows: when a left circularly polarized photon |L〉 passes along the −z direction through the cavity with QD spin prepared in the spin up and down superposed state 12(|+|), the resulting state will be electron and photon hybrid entangled state:
12(|+|)|L12(|,R+|,L).

The proposed system of hybrid entangler can be further generalized to parity check gate (PCG) based on two QDs embedded in two microcavities. One input photon passes into the cavity from the first to second one in −z direction. If the spin of the two electrons are not in the same direction, the photon will leave the cavity in the upper mode and trigger the detector which indicates that the parity of the particles is odd. Otherwise, if the two electrons are prepared in the state |↑〉|↑〉 or |↓〉|↓〉, the output photon will trigger the lower mode detector which indicates that the parity of the two particles is even.

Here we assume that the electron-spin in the cavity is prepared in the spin up and down superposed state |ϕs=12(|+|). The photon passes through the cavity and interacts with the electron, then the photon and spin in the cavity become entangled and the state can be described as follows:

|ϕs|ψph12(|s,Rp|s,Lp),
here |L〉 and |R〉 represent the left and right circularly polarized state. The generic error modes on photons can be described in three forms as follows: the bit-flip error mode, the phase-flip error mode and both the two error mode. The corresponding states with errors can be written as:
|ψs,p+=12(|,Rs,p+|,Ls,p)
|ϕs,p+=12(|,Ls,p+|,Rs,p)
|φs,p=12(|,Ls,p|,Rs,p)

At first, we discussed the purification process on the mixed ensemble with bit-flip errors. If the initial pure state ensemble is ρ=|ψs,pψs,p|, the bit-flip noise will effect on the photonic qubit and transform the |ψs,p state to |ϕs,p:

ρ=F|ψs,pψs,p|+(1F)|ϕs,pϕs,p|.
here the coefficient (1−F) indicates the probability that the photonic qubit takes place a bit-flip operation.

Figure 2 illustrates the setup for EPP based on hybrid entangled ensemble with bit-flip errors. In the following we will give the detailed analysis about the EPP process. Alice and Bob pick up two pairs of the entangled pairs from the ensemble ρ randomly. With probability F2, the two pairs are in the state |ψ1,2|ψ3,4, here the subscripts 1 and 3 denote the electrons in each entangled states owned by Alice and the subscripts 2 and 4 represent the photons in each state on Bob’s side. In the beginning of hybrid EPP, Alice produces the input photon in the left circularly polarized state |L〉. Then the ancillary photon passes through the two cavities and Bob performs the PCG operation on his two photons. The evolution of the composite system can be described as follows:

12(|,R|,L)(|,R|,L)|Lancilla=12(|,,R,R+|,,L,L|,,R,L|,,L,R)|Lancilla12[(|,,R,R+|,,L,L)|R+(|,,R,L+|,,L,R)|L].
If the two electron spins in the two optical microcavities are in the same state (both in the states |↑〉1|↑〉2 or |↓〉1|↓〉2), the mode information of the input photon will not changed and trigger the detector in the lower mode (D2). The evolution of the composite system can be written as:
|L|1|2|R|1|2,|L|1|2|R|1|2.
Otherwise, if the two electron spins are not in the same state, the mode of the photon will be changed and detected by the detector in the upper mode (D1):
|L|1|2|L|1|2,|L|1|2|L|1|2.
By detecting the output mode of the ancillary photon, one can distinguish the spin states of electron systems in the even number parity {|↑〉1|↑〉2, |↓〉1|↓〉2} or in the odd number parity {|↑〉1|↓〉2, |↓〉1|↑〉2}. If the photon reveals the detector D2, the state will collapse to 12(|,,R,R+|,,L,L). Then Alice measures the electron spin 2 in the basis |±X=12(|+|). If Bob’s detection records one photon event in D3 and Alice’s measurement is |+ X〉, the remaining state is |ψ1,2+. Otherwise, they get the state |ψ1,2.

 

Fig. 2 Schematic diagram showing the principle of hybrid EPP process. The input ancillary photon is in the opposite direction of the spin direction as defined. CPBS denotes the polarization beamsplitter in left and right circularly polarized mode. D1 and D2 represent single photon detectors. D3 represents the photon number resolving detection.

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Exploiting the setup shown in Fig. 2, if the initial two hybrid entangled pairs are in the state |ϕ1,2|ϕ3,4 with probability (1 − F)2, the setup will evolve the composite system as

12(|,L|,R)(|,L|,R)|Lancilla=12(|,,L,L+|,,R,R|,,L,R|,,R,L)|Lancilla12[(|,,L,L+|,,R,R)|R+(|,,L,R+|,,R,L)|L].
Bob’s parity check will reveal the detector D3 with one photon event and Alice’s ancillary photon will be detected in the |R〉. Under this condition, the state can not be distinguished by Alice and Bob with the case of |ψ1,2|ψ3,4 and the two pairs are preserved.

Similarly, the evolution of the other two terms |ϕ1,2|ψ3,4 and |ψ1,2|ϕ3,4 are described as

12(|,L|,R)(|,R|,L)|Lancilla=12(|,,L,R+|,,R,L|,,L,L|,,R,R)|Lancilla12[(|,,L,R+|,,R,L)|R+(|,,L,L+|,,R,R)|L]
and
12(|,R|,L)(|,L|,R)|Lancilla=12(|,,R,L+|,,L,R|,,R,R|,,L,L)|Lancilla12[(|,,R,L+|,,L,R)|R+(|,,R,R+|,,L,L)|L].

These two cases are appeared with probability F(1–F) and can be distinguished by the case that Alice’s ancillary photon is detected in the lower spatial mode and Bob’s parity check reveals two photon event or none photon event on his detector D3. These two cases are discarded after EPP and we can get a new ensemble ρ′ with the fidelity of

F=F2F2+(1F)2
which is larger than F when F > 1/2.

For the hybrid entangled state with phase-flip errors, one can introduce Hadamard operations on electron spin and photon polarization to change them into bit-flip errors. The evolution of the state of |ψ〉 and |ψ+〉 under Hadamard operations can be described as follows:

12(|,R|,L)HeHp12(|,R|,L),
and
12(|,R+|,L)HeHp12(|,L|,R)
It is obvious that the state with phase flip errors |ψ+〉 can be changed into the state |ϕ〉 by simply Hadamard operations acting on the two particles. Then the two users can perform the EPP on the bit-flip errors to purify the ensemble efficiently.

3. Efficiency and experiment feasibilities

The realization of hybrid EPP relies on the electrons and photons parity check processes. For the parity check on photons, it is necessary to use photon number resolving detectors. The current experiment process has realized photon number detection with a high probability [36]. The parity check on electron spins rely on the properties of QD and microcavity coupled system. Detectors with quantum efficiencies η can be modeled by placing the transmission coefficients η in front of ideal detectors. The performance of the QD and microcavity coupled system relative to the frequency detuning and the normalized coupling strength, we employed the coupling constant g to calculate the fidelity in the coupled system to test the performance of our proposed protocol.

Figure 3 illustrates the entanglement fidelities versus coupling strength in our proposed EPP. The purification fidelity relies on the coupling strength of the QD and microcavity. Line A, line B and line C represent the fidelity after EPP with the coupling constant of the QD with micro-cavity gA/κ = 1.2, gB/κ = 0.3 and gC/κ = 0.1, respectively. As show in this figure, weak coupling rapidly decrease the EPP fidelity lines. It is obvious that if the coupling strength is large than 1, the results of EPP in realistic systems is similarly with ideal conditions. If the cavity side leakage κs is taken into account, the entanglement fidelity after EPP with respect to the initial fidelity is described by the dotted line in Fig. 4. And the solid line represents the EPP fidelity with no leaky. The dotted line is the fidelity with cavity leaky rate κs = 0.05. As shown in this figure, the cavity leakage which generally decrease the entanglement fidelity in EPP.

 

Fig. 3 Schematic diagram showing the efficiency of hybrid EPP process. The solid line (line A) represents the EPP fidelity with g/κ=1.2. Line B and line C are for fidelity lines with coupling strength g/κ=0.3 and g/κ=0.1.

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Fig. 4 Schematic diagram showing the efficiency of hybrid EPP process in leaky cavity. The solid line represents the EPP fidelity with no leaky. The dotted line is the fidelity with cavity leaky rate κs = 0.05.

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State-of-the-art technology allows the realization of high quality QDs and optical microcavities. QD is considered to be an artificial atom in which Rabi oscillations have been observed between the first two energy levels of a QD [37,38]. Recently, some progresses have been made on optical spin manipulation in QDs [3941] which provide us an useful method in controlling the spin state and measurement.

The core techniques for realizing our EPP process in the system are the long coherence time of QDs and the strong coupling of the quantum-dot with the cavity. Recent experiments have shown that the coherence time of the GaAs or InAs based QDs is longer enough [42]. The near-unity reflectance and transmittance are due to the formation of the mixed exciton cavity modes of the system. In current experiments, the strongly coupled QD and microcavity system has been demonstrated recently in various microcavities and nanocavities [4346]. Ref. [43] reported that the coupling strength approaches to g = 0.5 in microcavity with diameter d = 1.5μm with the cavity leakage acceptable. The quality factors for the micropillars of the same size were increased to 4 × 104 for diameters below d = 2μm, corresponding to g/(κ + κs) ≈ 2.4 by improving the sample designs and fabrication [47]. The fidelity of the proposed EPP may decrease by a factor [1+exp(tTe)]/2 due to the spin decoherence, here Te is the spin coherence time and t is the cavity photon lifetime. The spin coherence time could be extended to μs using spin echo techniques [48, 49]. This implies the feasibility of our hybrid EPP using QD in microcavity system. Therefore the proposed schemes could be implemented with current technology.

4. Summary

In summary, we have theoretically studied QND measurement of spin parity with QD and cavity coupled system and proposed a hybrid entanglement purification protocol. The parity QND requires one ancillary photon and single photon detection. Thus the parity of entangled state can be transformed to the spatial mode of the ancillary photon and the CNOT operations are not needed. Based on electron spin PCG and linear optical devices, hybrid EPP can be realized in which the two nonlocal parties can purify the initial state with a high probability.

Based on the current experimental parameters, the present scheme exhibit a high feasibility to detect the spin parity without destroying them. Therefore the interaction of QD and cavity coupled system shows a great potential as a new platform for solid quantum optics and quantum information processing.

Acknowledgments

This work is supported by the National Fundamental Research Program Grant No. 2010CB923202, Specialized Research Fund for the Doctoral Program of Education Ministry of China No. 20090005120008, the Fundamental Research Funds for the Central Universities No. BUPT2009RC0710, China National Natural Science Foundation Grant Nos. 10947151, 60937003.

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41. A. Greilich, S. E. Economou, S. Spatzek, D. R. Yakovlev, D. Reuter, A. D. Wieck, T. L. Reinecke, and M. Bayer, “Ultrafast optical rotations of electron spins in quantum dots,” Nature Physics 5, 262–266 (2009). [CrossRef]  

42. X. D. Xu, W. Yao, B. Sun, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Optically controlled locking of the nuclear field via coherent dark-state spectroscopy,” Nature 459, 1105–1109 (2009). [CrossRef]   [PubMed]  

43. J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004). [CrossRef]   [PubMed]  

44. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004). [CrossRef]   [PubMed]  

45. E. Peter, P. Senellart, D. Martrou, A. Lematre, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 067401 (2005). [CrossRef]   [PubMed]  

46. E. Abe, H. Wu, A. Ardavan, and J.J. L. Morton, “Electron spin ensemble strongly coupled to a three-dimensional microwave cavity,” App. Phys. Lett. 98, 251108 (2011). [CrossRef]  

47. S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauβ, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150.000,” App. Phys. Lett. 90, 251109 (2007). [CrossRef]  

48. S. M. Clark, K.-M. C. Fu, Q. Zhang, T. D. Ladd, C. Stanley, and Y. Yamamoto, “Ultrafast optical spin echo for electron spins in semiconductors,” Phys. Rev. Lett. 102, 247601 (2009). [CrossRef]   [PubMed]  

49. D. Press, K. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nature Photonics 4, 367–370 (2010). [CrossRef]  

References

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  2. C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bells theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
    [CrossRef] [PubMed]
  3. C. H. Bennett and S. J. Wiesner, “Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
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  4. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
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  5. L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
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  6. B. Zhao, Z. B. Chen, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Robust creation of entanglement between remote memory qubits,” Phys. Rev. Lett. 98, 240502 (2007).
    [CrossRef] [PubMed]
  7. N. Sangouard, C. Simon, H. Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80 (2011).
    [CrossRef]
  8. G. -L. Long and X. -S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
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  9. F. -G. Deng, G. -L. Long, and X. -S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A 68, 042317 (2003).
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  10. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
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  14. J. W. Pan, S. Gasparonl, R. Ursin, G. Weihs, and A. Zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature 423, 417–422 (2003).
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  15. C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. 89, 257901 (2002).
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  16. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A 77, 042308 (2008).
    [CrossRef]
  17. L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77, 042315 (2008).
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  18. Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
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  20. M. Murao, M. B. Plenio, S. Popescu, and V. Vedral, “Multiparticle entanglement purification protocols,” and P. L. Knight, Phys. Rev. A 57, R4075–R4078 (1998).
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  22. Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
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  25. C. Y. Hu, W. J. Munro, J. L. O’Brien, and J. G. Rarity, “Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity,” Phys. Rev. B 80, 205326 (2009).
    [CrossRef]
  26. C. Y. Hu, W. J. Munro, and J. G. Rarity, “Deterministic photon entangler using a charged quantum dot inside a microcavity,” Phys. Rev. B 78, 125318 (2008).
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  27. C. Y. Hu and J. G. Rarity, “Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity,”, Phys. Rev. B 83, 115303 (2011).
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  28. A. Auffèves-Garnier, C. Simon, J. M. Gérard, and J. P. Poizat, “Giant optical nonlinearity induced by a single two-level system interacting with a cavity in the Purcell regime,”, Phys. Rev. A 75, 053823 (2007).
    [CrossRef]
  29. P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater using bright coherent light,” Phys. Rev. Lett. 96, 240501 (2006).
    [CrossRef] [PubMed]
  30. K. Azuma, N. Sota, R. Namiki, S. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Optimal entanglement generation for efficient hybrid quantum repeaters,” Phys. Rev. A 80, 060303(R) (2009).
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  31. E. Waks and C. Monroe, “Protocol for hybrid entanglement between a trapped atom and a quantum dot,” Phys. Rev. A 80, 062330 (2009).
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  32. J. B. Brask, I. Rigas, E. S. Polzik, U. L. Andersen, and A. S. Sørensen, “Hybrid long-distance entanglement distribution protocol,” Phys. Rev. Lett. 105, 160501 (2010).
    [CrossRef]
  33. C. Y. Hu, A. Young, J. L. O’Brien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon,” Phys. Rev. B 78, 085307 (2008).
    [CrossRef]
  34. A. B. Young, R. Oulton, C. Y. Hu, A. C. T. Thijssen, C. Schneider, S. Reitzenstein, M. Kamp, S. Höfling, L. Worschech, A. Forchel, and J. G. Rarity, “Quantum-dot-induced phase shift in a pillar microcavity,” Phys. Rev. A 84, 011803(R) (2011).
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  35. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin Heidelberg, 1994).
  36. Y. -F. Xiao, S.K. Özdemir, V. Gaddam, C. H. Dong, N. Imoto, and L. Yang, “Quantum nondemolition measurement of photon number via optical Kerr effect in an ultra-high-Q microtoroid cavity,” Opt. Exp. 16, 21462–21475 (2008).
    [CrossRef]
  37. T. H. Stievater, X. Q. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “Rabi oscillations of excitons in single quantum dots,”, Phys. Rev. Lett. 87, 133603 (2001).
    [CrossRef] [PubMed]
  38. H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, “Exciton rabi oscillation in a single quantum dot,” Phys. Rev. Lett. 87, 246401 (2001).
    [CrossRef] [PubMed]
  39. J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,” Science 320, 349–352 (2008).
    [CrossRef] [PubMed]
  40. D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456, 218–221 (2008).
    [CrossRef] [PubMed]
  41. A. Greilich, S. E. Economou, S. Spatzek, D. R. Yakovlev, D. Reuter, A. D. Wieck, T. L. Reinecke, and M. Bayer, “Ultrafast optical rotations of electron spins in quantum dots,” Nature Physics 5, 262–266 (2009).
    [CrossRef]
  42. X. D. Xu, W. Yao, B. Sun, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Optically controlled locking of the nuclear field via coherent dark-state spectroscopy,” Nature 459, 1105–1109 (2009).
    [CrossRef] [PubMed]
  43. J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
    [CrossRef] [PubMed]
  44. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
    [CrossRef] [PubMed]
  45. E. Peter, P. Senellart, D. Martrou, A. Lematre, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 067401 (2005).
    [CrossRef] [PubMed]
  46. E. Abe, H. Wu, A. Ardavan, and J.J. L. Morton, “Electron spin ensemble strongly coupled to a three-dimensional microwave cavity,” App. Phys. Lett. 98, 251108 (2011).
    [CrossRef]
  47. S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauβ, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150.000,” App. Phys. Lett. 90, 251109 (2007).
    [CrossRef]
  48. S. M. Clark, K.-M. C. Fu, Q. Zhang, T. D. Ladd, C. Stanley, and Y. Yamamoto, “Ultrafast optical spin echo for electron spins in semiconductors,” Phys. Rev. Lett. 102, 247601 (2009).
    [CrossRef] [PubMed]
  49. D. Press, K. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nature Photonics 4, 367–370 (2010).
    [CrossRef]

2011 (5)

N. Sangouard, C. Simon, H. Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80 (2011).
[CrossRef]

F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A 83, 062316 (2011).
[CrossRef]

C. Y. Hu and J. G. Rarity, “Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity,”, Phys. Rev. B 83, 115303 (2011).
[CrossRef]

A. B. Young, R. Oulton, C. Y. Hu, A. C. T. Thijssen, C. Schneider, S. Reitzenstein, M. Kamp, S. Höfling, L. Worschech, A. Forchel, and J. G. Rarity, “Quantum-dot-induced phase shift in a pillar microcavity,” Phys. Rev. A 84, 011803(R) (2011).
[CrossRef]

E. Abe, H. Wu, A. Ardavan, and J.J. L. Morton, “Electron spin ensemble strongly coupled to a three-dimensional microwave cavity,” App. Phys. Lett. 98, 251108 (2011).
[CrossRef]

2010 (6)

D. Press, K. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nature Photonics 4, 367–370 (2010).
[CrossRef]

J. B. Brask, I. Rigas, E. S. Polzik, U. L. Andersen, and A. S. Sørensen, “Hybrid long-distance entanglement distribution protocol,” Phys. Rev. Lett. 105, 160501 (2010).
[CrossRef]

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. -P. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[CrossRef] [PubMed]

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[CrossRef]

X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
[CrossRef]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[CrossRef]

2009 (6)

C. Y. Hu, W. J. Munro, J. L. O’Brien, and J. G. Rarity, “Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity,” Phys. Rev. B 80, 205326 (2009).
[CrossRef]

K. Azuma, N. Sota, R. Namiki, S. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Optimal entanglement generation for efficient hybrid quantum repeaters,” Phys. Rev. A 80, 060303(R) (2009).
[CrossRef]

E. Waks and C. Monroe, “Protocol for hybrid entanglement between a trapped atom and a quantum dot,” Phys. Rev. A 80, 062330 (2009).
[CrossRef]

A. Greilich, S. E. Economou, S. Spatzek, D. R. Yakovlev, D. Reuter, A. D. Wieck, T. L. Reinecke, and M. Bayer, “Ultrafast optical rotations of electron spins in quantum dots,” Nature Physics 5, 262–266 (2009).
[CrossRef]

X. D. Xu, W. Yao, B. Sun, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Optically controlled locking of the nuclear field via coherent dark-state spectroscopy,” Nature 459, 1105–1109 (2009).
[CrossRef] [PubMed]

S. M. Clark, K.-M. C. Fu, Q. Zhang, T. D. Ladd, C. Stanley, and Y. Yamamoto, “Ultrafast optical spin echo for electron spins in semiconductors,” Phys. Rev. Lett. 102, 247601 (2009).
[CrossRef] [PubMed]

2008 (7)

C. Y. Hu, A. Young, J. L. O’Brien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon,” Phys. Rev. B 78, 085307 (2008).
[CrossRef]

J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,” Science 320, 349–352 (2008).
[CrossRef] [PubMed]

D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456, 218–221 (2008).
[CrossRef] [PubMed]

Y. -F. Xiao, S.K. Özdemir, V. Gaddam, C. H. Dong, N. Imoto, and L. Yang, “Quantum nondemolition measurement of photon number via optical Kerr effect in an ultra-high-Q microtoroid cavity,” Opt. Exp. 16, 21462–21475 (2008).
[CrossRef]

C. Y. Hu, W. J. Munro, and J. G. Rarity, “Deterministic photon entangler using a charged quantum dot inside a microcavity,” Phys. Rev. B 78, 125318 (2008).
[CrossRef]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A 77, 042308 (2008).
[CrossRef]

L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77, 042315 (2008).
[CrossRef]

2007 (4)

B. Zhao, Z. B. Chen, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Robust creation of entanglement between remote memory qubits,” Phys. Rev. Lett. 98, 240502 (2007).
[CrossRef] [PubMed]

Y. W. Cheong, S. W. Lee, J. Lee, and H. W. Lee, “Entanglement purification for high-dimensional multipartite systems,” Phys. Rev. A 76, 042314 (2007).
[CrossRef]

A. Auffèves-Garnier, C. Simon, J. M. Gérard, and J. P. Poizat, “Giant optical nonlinearity induced by a single two-level system interacting with a cavity in the Purcell regime,”, Phys. Rev. A 75, 053823 (2007).
[CrossRef]

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauβ, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150.000,” App. Phys. Lett. 90, 251109 (2007).
[CrossRef]

2006 (1)

P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater using bright coherent light,” Phys. Rev. Lett. 96, 240501 (2006).
[CrossRef] [PubMed]

2005 (1)

E. Peter, P. Senellart, D. Martrou, A. Lematre, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 067401 (2005).
[CrossRef] [PubMed]

2004 (2)

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[CrossRef] [PubMed]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef] [PubMed]

2003 (2)

J. W. Pan, S. Gasparonl, R. Ursin, G. Weihs, and A. Zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature 423, 417–422 (2003).
[CrossRef] [PubMed]

F. -G. Deng, G. -L. Long, and X. -S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A 68, 042317 (2003).
[CrossRef]

2002 (2)

C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. 89, 257901 (2002).
[CrossRef] [PubMed]

G. -L. Long and X. -S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
[CrossRef]

2001 (4)

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[CrossRef] [PubMed]

J. W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
[CrossRef] [PubMed]

T. H. Stievater, X. Q. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “Rabi oscillations of excitons in single quantum dots,”, Phys. Rev. Lett. 87, 133603 (2001).
[CrossRef] [PubMed]

H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, “Exciton rabi oscillation in a single quantum dot,” Phys. Rev. Lett. 87, 246401 (2001).
[CrossRef] [PubMed]

2000 (1)

H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (2000).
[CrossRef]

1998 (1)

M. Murao, M. B. Plenio, S. Popescu, and V. Vedral, “Multiparticle entanglement purification protocols,” and P. L. Knight, Phys. Rev. A 57, R4075–R4078 (1998).
[CrossRef]

1997 (1)

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

1996 (2)

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[CrossRef] [PubMed]

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[CrossRef] [PubMed]

1992 (2)

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bells theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[CrossRef] [PubMed]

C. H. Bennett and S. J. Wiesner, “Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[CrossRef] [PubMed]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[CrossRef] [PubMed]

Abe, E.

E. Abe, H. Wu, A. Ardavan, and J.J. L. Morton, “Electron spin ensemble strongly coupled to a three-dimensional microwave cavity,” App. Phys. Lett. 98, 251108 (2011).
[CrossRef]

Andersen, U. L.

J. B. Brask, I. Rigas, E. S. Polzik, U. L. Andersen, and A. S. Sørensen, “Hybrid long-distance entanglement distribution protocol,” Phys. Rev. Lett. 105, 160501 (2010).
[CrossRef]

Ando, H.

H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, “Exciton rabi oscillation in a single quantum dot,” Phys. Rev. Lett. 87, 246401 (2001).
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X. D. Xu, W. Yao, B. Sun, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Optically controlled locking of the nuclear field via coherent dark-state spectroscopy,” Nature 459, 1105–1109 (2009).
[CrossRef] [PubMed]

Takagahara, T.

H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, “Exciton rabi oscillation in a single quantum dot,” Phys. Rev. Lett. 87, 246401 (2001).
[CrossRef] [PubMed]

Temmyo, J.

H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, “Exciton rabi oscillation in a single quantum dot,” Phys. Rev. Lett. 87, 246401 (2001).
[CrossRef] [PubMed]

Thijssen, A. C. T.

A. B. Young, R. Oulton, C. Y. Hu, A. C. T. Thijssen, C. Schneider, S. Reitzenstein, M. Kamp, S. Höfling, L. Worschech, A. Forchel, and J. G. Rarity, “Quantum-dot-induced phase shift in a pillar microcavity,” Phys. Rev. A 84, 011803(R) (2011).
[CrossRef]

Ursin, R.

J. W. Pan, S. Gasparonl, R. Ursin, G. Weihs, and A. Zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature 423, 417–422 (2003).
[CrossRef] [PubMed]

van Exter, M. P.

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. -P. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[CrossRef] [PubMed]

van Loock, P.

P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater using bright coherent light,” Phys. Rev. Lett. 96, 240501 (2006).
[CrossRef] [PubMed]

Vedral, V.

M. Murao, M. B. Plenio, S. Popescu, and V. Vedral, “Multiparticle entanglement purification protocols,” and P. L. Knight, Phys. Rev. A 57, R4075–R4078 (1998).
[CrossRef]

Waks, E.

E. Waks and C. Monroe, “Protocol for hybrid entanglement between a trapped atom and a quantum dot,” Phys. Rev. A 80, 062330 (2009).
[CrossRef]

Walls, D. F.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin Heidelberg, 1994).

Wang, C.

L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77, 042315 (2008).
[CrossRef]

Weihs, G.

J. W. Pan, S. Gasparonl, R. Ursin, G. Weihs, and A. Zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature 423, 417–422 (2003).
[CrossRef] [PubMed]

Weinfurter, H.

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

Wieck, A. D.

A. Greilich, S. E. Economou, S. Spatzek, D. R. Yakovlev, D. Reuter, A. D. Wieck, T. L. Reinecke, and M. Bayer, “Ultrafast optical rotations of electron spins in quantum dots,” Nature Physics 5, 262–266 (2009).
[CrossRef]

Wiesner, S. J.

C. H. Bennett and S. J. Wiesner, “Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[CrossRef] [PubMed]

Wootters, W. K.

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
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Worschech, L.

A. B. Young, R. Oulton, C. Y. Hu, A. C. T. Thijssen, C. Schneider, S. Reitzenstein, M. Kamp, S. Höfling, L. Worschech, A. Forchel, and J. G. Rarity, “Quantum-dot-induced phase shift in a pillar microcavity,” Phys. Rev. A 84, 011803(R) (2011).
[CrossRef]

Wu, H.

E. Abe, H. Wu, A. Ardavan, and J.J. L. Morton, “Electron spin ensemble strongly coupled to a three-dimensional microwave cavity,” App. Phys. Lett. 98, 251108 (2011).
[CrossRef]

Xiao, L.

L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77, 042315 (2008).
[CrossRef]

Xiao, Y. -F.

Y. -F. Xiao, S.K. Özdemir, V. Gaddam, C. H. Dong, N. Imoto, and L. Yang, “Quantum nondemolition measurement of photon number via optical Kerr effect in an ultra-high-Q microtoroid cavity,” Opt. Exp. 16, 21462–21475 (2008).
[CrossRef]

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X. D. Xu, W. Yao, B. Sun, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Optically controlled locking of the nuclear field via coherent dark-state spectroscopy,” Nature 459, 1105–1109 (2009).
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A. Greilich, S. E. Economou, S. Spatzek, D. R. Yakovlev, D. Reuter, A. D. Wieck, T. L. Reinecke, and M. Bayer, “Ultrafast optical rotations of electron spins in quantum dots,” Nature Physics 5, 262–266 (2009).
[CrossRef]

Yamaguchi, F.

P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater using bright coherent light,” Phys. Rev. Lett. 96, 240501 (2006).
[CrossRef] [PubMed]

Yamamoto, T.

K. Azuma, N. Sota, R. Namiki, S. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Optimal entanglement generation for efficient hybrid quantum repeaters,” Phys. Rev. A 80, 060303(R) (2009).
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Yamamoto, Y.

D. Press, K. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nature Photonics 4, 367–370 (2010).
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S. M. Clark, K.-M. C. Fu, Q. Zhang, T. D. Ladd, C. Stanley, and Y. Yamamoto, “Ultrafast optical spin echo for electron spins in semiconductors,” Phys. Rev. Lett. 102, 247601 (2009).
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D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456, 218–221 (2008).
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P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater using bright coherent light,” Phys. Rev. Lett. 96, 240501 (2006).
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Yang, L.

Y. -F. Xiao, S.K. Özdemir, V. Gaddam, C. H. Dong, N. Imoto, and L. Yang, “Quantum nondemolition measurement of photon number via optical Kerr effect in an ultra-high-Q microtoroid cavity,” Opt. Exp. 16, 21462–21475 (2008).
[CrossRef]

Yao, W.

X. D. Xu, W. Yao, B. Sun, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Optically controlled locking of the nuclear field via coherent dark-state spectroscopy,” Nature 459, 1105–1109 (2009).
[CrossRef] [PubMed]

Yoshie, T.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef] [PubMed]

Young, A.

C. Y. Hu, A. Young, J. L. O’Brien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon,” Phys. Rev. B 78, 085307 (2008).
[CrossRef]

Young, A. B.

A. B. Young, R. Oulton, C. Y. Hu, A. C. T. Thijssen, C. Schneider, S. Reitzenstein, M. Kamp, S. Höfling, L. Worschech, A. Forchel, and J. G. Rarity, “Quantum-dot-induced phase shift in a pillar microcavity,” Phys. Rev. A 84, 011803(R) (2011).
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Zeilinger, A.

J. W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
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D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

Zellinger, A.

J. W. Pan, S. Gasparonl, R. Ursin, G. Weihs, and A. Zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature 423, 417–422 (2003).
[CrossRef] [PubMed]

Zhang, B.

D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456, 218–221 (2008).
[CrossRef] [PubMed]

Zhang, Q.

S. M. Clark, K.-M. C. Fu, Q. Zhang, T. D. Ladd, C. Stanley, and Y. Yamamoto, “Ultrafast optical spin echo for electron spins in semiconductors,” Phys. Rev. Lett. 102, 247601 (2009).
[CrossRef] [PubMed]

Zhang, W.

L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77, 042315 (2008).
[CrossRef]

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B. Zhao, Z. B. Chen, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Robust creation of entanglement between remote memory qubits,” Phys. Rev. Lett. 98, 240502 (2007).
[CrossRef] [PubMed]

Zhou, H. Y.

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A 77, 042308 (2008).
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L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
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H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (2000).
[CrossRef]

App. Phys. Lett. (2)

E. Abe, H. Wu, A. Ardavan, and J.J. L. Morton, “Electron spin ensemble strongly coupled to a three-dimensional microwave cavity,” App. Phys. Lett. 98, 251108 (2011).
[CrossRef]

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauβ, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150.000,” App. Phys. Lett. 90, 251109 (2007).
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Nature (8)

D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456, 218–221 (2008).
[CrossRef] [PubMed]

X. D. Xu, W. Yao, B. Sun, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Optically controlled locking of the nuclear field via coherent dark-state spectroscopy,” Nature 459, 1105–1109 (2009).
[CrossRef] [PubMed]

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[CrossRef] [PubMed]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
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D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[CrossRef] [PubMed]

J. W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
[CrossRef] [PubMed]

J. W. Pan, S. Gasparonl, R. Ursin, G. Weihs, and A. Zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature 423, 417–422 (2003).
[CrossRef] [PubMed]

Nature Photonics (1)

D. Press, K. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nature Photonics 4, 367–370 (2010).
[CrossRef]

Nature Physics (1)

A. Greilich, S. E. Economou, S. Spatzek, D. R. Yakovlev, D. Reuter, A. D. Wieck, T. L. Reinecke, and M. Bayer, “Ultrafast optical rotations of electron spins in quantum dots,” Nature Physics 5, 262–266 (2009).
[CrossRef]

Opt. Exp. (1)

Y. -F. Xiao, S.K. Özdemir, V. Gaddam, C. H. Dong, N. Imoto, and L. Yang, “Quantum nondemolition measurement of photon number via optical Kerr effect in an ultra-high-Q microtoroid cavity,” Opt. Exp. 16, 21462–21475 (2008).
[CrossRef]

Phys. Rev. A (14)

K. Azuma, N. Sota, R. Namiki, S. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Optimal entanglement generation for efficient hybrid quantum repeaters,” Phys. Rev. A 80, 060303(R) (2009).
[CrossRef]

E. Waks and C. Monroe, “Protocol for hybrid entanglement between a trapped atom and a quantum dot,” Phys. Rev. A 80, 062330 (2009).
[CrossRef]

A. B. Young, R. Oulton, C. Y. Hu, A. C. T. Thijssen, C. Schneider, S. Reitzenstein, M. Kamp, S. Höfling, L. Worschech, A. Forchel, and J. G. Rarity, “Quantum-dot-induced phase shift in a pillar microcavity,” Phys. Rev. A 84, 011803(R) (2011).
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A. Auffèves-Garnier, C. Simon, J. M. Gérard, and J. P. Poizat, “Giant optical nonlinearity induced by a single two-level system interacting with a cavity in the Purcell regime,”, Phys. Rev. A 75, 053823 (2007).
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F. -G. Deng, G. -L. Long, and X. -S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A 68, 042317 (2003).
[CrossRef]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A 77, 042308 (2008).
[CrossRef]

L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77, 042315 (2008).
[CrossRef]

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[CrossRef]

X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
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M. Murao, M. B. Plenio, S. Popescu, and V. Vedral, “Multiparticle entanglement purification protocols,” and P. L. Knight, Phys. Rev. A 57, R4075–R4078 (1998).
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Y. W. Cheong, S. W. Lee, J. Lee, and H. W. Lee, “Entanglement purification for high-dimensional multipartite systems,” Phys. Rev. A 76, 042314 (2007).
[CrossRef]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
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F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A 83, 062316 (2011).
[CrossRef]

Phys. Rev. B (4)

C. Y. Hu, W. J. Munro, J. L. O’Brien, and J. G. Rarity, “Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity,” Phys. Rev. B 80, 205326 (2009).
[CrossRef]

C. Y. Hu, W. J. Munro, and J. G. Rarity, “Deterministic photon entangler using a charged quantum dot inside a microcavity,” Phys. Rev. B 78, 125318 (2008).
[CrossRef]

C. Y. Hu and J. G. Rarity, “Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity,”, Phys. Rev. B 83, 115303 (2011).
[CrossRef]

C. Y. Hu, A. Young, J. L. O’Brien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon,” Phys. Rev. B 78, 085307 (2008).
[CrossRef]

Phys. Rev. Lett. (15)

S. M. Clark, K.-M. C. Fu, Q. Zhang, T. D. Ladd, C. Stanley, and Y. Yamamoto, “Ultrafast optical spin echo for electron spins in semiconductors,” Phys. Rev. Lett. 102, 247601 (2009).
[CrossRef] [PubMed]

E. Peter, P. Senellart, D. Martrou, A. Lematre, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 067401 (2005).
[CrossRef] [PubMed]

P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater using bright coherent light,” Phys. Rev. Lett. 96, 240501 (2006).
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C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. 89, 257901 (2002).
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A. K. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
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J. B. Brask, I. Rigas, E. S. Polzik, U. L. Andersen, and A. S. Sørensen, “Hybrid long-distance entanglement distribution protocol,” Phys. Rev. Lett. 105, 160501 (2010).
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H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, “Exciton rabi oscillation in a single quantum dot,” Phys. Rev. Lett. 87, 246401 (2001).
[CrossRef] [PubMed]

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. -P. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
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D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
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H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (2000).
[CrossRef]

B. Zhao, Z. B. Chen, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Robust creation of entanglement between remote memory qubits,” Phys. Rev. Lett. 98, 240502 (2007).
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Rev. Mod. Phys. (1)

N. Sangouard, C. Simon, H. Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80 (2011).
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Science (1)

J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,” Science 320, 349–352 (2008).
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Other (1)

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin Heidelberg, 1994).

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Figures (4)

Fig. 1
Fig. 1

Schematic of QD and microcavity coupled system. The diagram shows the principle of hybrid entanglement generation in quantum dot and cavity coupled system.

Fig. 2
Fig. 2

Schematic diagram showing the principle of hybrid EPP process. The input ancillary photon is in the opposite direction of the spin direction as defined. CPBS denotes the polarization beamsplitter in left and right circularly polarized mode. D1 and D2 represent single photon detectors. D3 represents the photon number resolving detection.

Fig. 3
Fig. 3

Schematic diagram showing the efficiency of hybrid EPP process. The solid line (line A) represents the EPP fidelity with g/κ=1.2. Line B and line C are for fidelity lines with coupling strength g/κ=0.3 and g/κ=0.1.

Fig. 4
Fig. 4

Schematic diagram showing the efficiency of hybrid EPP process in leaky cavity. The solid line represents the EPP fidelity with no leaky. The dotted line is the fidelity with cavity leaky rate κs = 0.05.

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

d a ^ d t = [ i ( ω C ω ) + κ + κ s 2 ] a ^ g σ κ a ^ i n κ a ^ i n + H ^
d σ d t = [ i ( ω X ω ) + γ 2 ] σ g σ z a ^ + G ^
a ^ r = a ^ i n + κ a ^ a ^ t = a ^ i n + κ a ^
r ( ω ) = [ i ( ω X ω ) + γ 2 ] [ i ( ω c ω ) + κ s 2 ] + g 2 [ i ( ω X ω ) + γ 2 ] [ i ( ω c ω ) + κ + κ s 2 ] + g 2 t ( ω ) = κ [ i ( ω X ω ) + γ 2 ] [ i ( ω X ω ) + γ 2 ] [ i ( ω c ω ) + κ + κ s 2 ] + g 2 .
r 0 ( ω ) = i ( ω 0 ω ) + κ s 2 i ( ω 0 ω ) + κ s 2 + κ t 0 ( ω ) = κ i ( ω 0 ω ) + κ s 2 + κ .
| R , | L , , | L , | L , , | R , | R , , | L , | R , , | R , | R , , | L , | R , , | R , | L , , | L , | L , ,
1 2 ( | + | ) | L 1 2 ( | , R + | , L ) .
| ϕ s | ψ p h 1 2 ( | s , R p | s , L p ) ,
| ψ s , p + = 1 2 ( | , R s , p + | , L s , p )
| ϕ s , p + = 1 2 ( | , L s , p + | , R s , p )
| φ s , p = 1 2 ( | , L s , p | , R s , p )
ρ = F | ψ s , p ψ s , p | + ( 1 F ) | ϕ s , p ϕ s , p | .
1 2 ( | , R | , L ) ( | , R | , L ) | L ancilla = 1 2 ( | , , R , R + | , , L , L | , , R , L | , , L , R ) | L ancilla 1 2 [ ( | , , R , R + | , , L , L ) | R + ( | , , R , L + | , , L , R ) | L ] .
| L | 1 | 2 | R | 1 | 2 , | L | 1 | 2 | R | 1 | 2 .
| L | 1 | 2 | L | 1 | 2 , | L | 1 | 2 | L | 1 | 2 .
1 2 ( | , L | , R ) ( | , L | , R ) | L ancilla = 1 2 ( | , , L , L + | , , R , R | , , L , R | , , R , L ) | L ancilla 1 2 [ ( | , , L , L + | , , R , R ) | R + ( | , , L , R + | , , R , L ) | L ] .
1 2 ( | , L | , R ) ( | , R | , L ) | L ancilla = 1 2 ( | , , L , R + | , , R , L | , , L , L | , , R , R ) | L ancilla 1 2 [ ( | , , L , R + | , , R , L ) | R + ( | , , L , L + | , , R , R ) | L ]
1 2 ( | , R | , L ) ( | , L | , R ) | L ancilla = 1 2 ( | , , R , L + | , , L , R | , , R , R | , , L , L ) | L ancilla 1 2 [ ( | , , R , L + | , , L , R ) | R + ( | , , R , R + | , , L , L ) | L ] .
F = F 2 F 2 + ( 1 F ) 2
1 2 ( | , R | , L ) H e H p 1 2 ( | , R | , L ) ,
1 2 ( | , R + | , L ) H e H p 1 2 ( | , L | , R )

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