Abstract

Hybrid entangled states exhibit entanglement between different degrees of freedom of a particle pair and thus could be useful for asymmetric optical quantum network where the communication channels are characterized by different properties. We report the first experimental realization of hybrid polarization-orbital angular momentum (OAM) entangled states by adopting a spontaneous parametric down conversion source of polarization entangled states and a polarization-OAM transferrer. The generated quantum states have been characterized through quantum state tomography. Finally, the violation of Bell’s inequalities with the hybrid two photon system has been observed.

© 2010 Optical Society of America

1. Introduction

The development of tailored photonic sources suitable to produce entanglement represents a crucial resource for quantum information applications like quantum communication schemes, quantum cryptographic protocols, and for fundamental tests of quantum theory [1]. Parametric down conversion has been proven to be the best source of entangled photon pairs so far in an ever increasing number of experiments on the foundations of quantum mechanics and in the new field of quantum communication [2]. Optical implementation of quantum information processing have been realized by several, different approaches, each one with its own advantages and limitations concerning the generation, manipulation, transmission, detection, robustness of the information carriers. While initially most of the effort has been devoted to the implementation of polarization entangled states [3–5], in the last few years entangling different degrees of freedom has attracted much attention. Within this scenario, the orbital angular momentum (OAM), the degree of freedom of light associated with rotationally structured transverse spatial modes, has been recently exploited to encode quantum states [6–9]. Generation of OAM-entangled pairs of photons has been demonstrated mainly by spontaneous parametric down-conversion [10–18]. By merging different techniques, it is possible to exploit the power and the advantages of each method and hence overcome the present technological limitations.

Hybrid entangled states exhibit entanglement between different degrees of freedom of a particle pair. The generation of such states can be useful for asymmetric optical quantum network where the different communication channels adopted for transmitting quantum information exhibit different properties. In such a way one could adopt the suitable degree of freedom with larger robustness along the channel. From a fundamental point of view, the observation of non-locality with hybrid systems proves the fundamental independence of entanglement from the physical realization of the adopted Hilbert space. Very recently the hybrid entanglement of photon pairs between the path (linear momentum) of one photon and the polarization of the other photon has been reported by two different techniques [19, 20]. Nevertheless, the capability of generating hybrid-entangled state encoded in the polarization and OAM of single photons could be advantageous since it could allow the engineering of qubit-qudit entangled states, related to the different Hilbert space dimensionality of the two degrees of freedom. It has been pointed out that such states are desiderable for quantum information and communication protocols, as quantum teleportation, and for the possibility to send quantum information through an optical quantum network composed by optical fiber channels and free-space [20, 21].

 

Fig. 1. Experimental setup adopted for the generation and characterization of hybrid π-OAM entangled states.(A)Generation of polarization entangled photons on modes kA and kB.(B)Projection on the OAM state with m = 0 through the coupling on a single mode fiber (SMF).(C)Encoding of the state in the OAM subspace o 2 through the πo 2 transferrer.

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In this paper, we report the experimental realization of hybrid polarization-OAM entangled states, by adopting the deterministic polarization-OAM transferrer introduced in Ref. [22, 23]. Polarization entangled photon pairs are created by spontaneous parametric down conversion, the spatial profile of the twin photons is filtered through single mode fibers and finally the polarization is coherently transferred to OAM state for one photon. A complete characterization of the hybrid entangled quantum states has been carried out by adopting the quantum state tomography technique. This result, together with the achieved generation rate, the easiness of alignment and the high quality of the generated state, can make this optical source a powerful tool for advanced quantum information tasks. For instance the OAM features can be more appropriate for mapping single photon states in atomic systems.

2. Experimental apparaturs and generation of hybrid states

Let us now describe the experimental layout shown in Fig. 1. A 1.5mm thick β-barium borate crystal (BBO) cut for type-II phase matching [3], is pumped by the second harmonic of a Ti:Sa mode-locked laser beam, and generates via spontaneous parametric fluorescence polarization entangled photon pairs on modes kA and kB with wavelength λ = 795 nm, and pulse bandwidth ∆λ = 4.5 nm, as determined by two interference filters (IF). The spatial and temporal walk-off is compensated by inserting a λ2 waveplate and a 0.75 mm thick BBO crystal (SC) on each output mode kA and kB [3]. Thus the source generates photon pair in the singlet entangled state encoded in the polarization, i.e. 12(HAVBVAHB) . The photon generated on mode kA is sent through a standard polarization analysis setup and then coupled to a single mode fiber connected to the single-photon counter modules (SPCM) DA. The photon generated on mode kB is coupled to a single mode fiber, in order to collapse its transverse spatial mode into a pure TEM00, corresponding to OAM m = 0. After the fiber output, two waveplates compensate (CP) the polarization rotation introduced by the fiber. To transform the polarization entangled pairs into an hybrid entangled state the photon B is sent through the quantum transferrer πo 2, which transfers the polarization quantum states in the OAM degree of freedom.

 

Fig. 2. Experimental density matrix of the hybrid entangled state generated after the transferrer transformation on photons on kB mode. Each measurement setting lasted 15s.

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The quantum transferrers have been extensively described in [22, 23]. To sum up, the transformation φπ0oHπφo2 carried out by the transferrer, is achieved through a q-plate device, which couples the spinorial (polarization) and orbital contributions of the angular momentum of photons [22, 24]. Here and after, we will denote the bidimensional OAM subspace with m = ±2, where m denotes here the OAM per photon along the beam axis in units of , as o 2 = {∣ + 2〉, ∣ − 2〉}. According to the nomenclature φπϕo2 , the ∣·〉π and ·o2 stand for the photon quantum state ‘kets’ in the polarization and OAM degrees of freedom. Following the same convention, the OAM equivalent of the two basis linear polarizations ∣H〉 and ∣V〉 are then defined as ∣h〉 = (2−1/2)(∣ + 2〉 + ∣ − 2〉); ∣ν〉 = (2−1/2)(∣ + 2〉 − ∣ − 2〉). Finally, the ±45° angle “anti-diagonal” and “diagonal” linear polarizations will be hereafter denoted with the kets ∣ + 〉 = (2−1/2)(∣H〉 + ∣V〉) and ∣ − 〉 = (2−1/2)(∣H〉 − ∣V〉), and the corresponding OAM states are defined analogously: ∣a〉 = e −iπ/4(∣ + 2〉 + i∣ − 2〉)(2−1/2); ∣d〉 = e/4(∣ + 2〉 − i∣ − 2〉)(2−1/2). The transformation established by a q-plate with q = 1, as the one adopted in our experiment, can be described as:

Lπ0oQPRπ+2o2
Rπ0oQPLπ2o2

where L and R denote the left and right circular polarization states, respectively. Any coherent superposition of the two input states given in Eq. (1) is preserved by the QP transformation, leading to the equivalent superposition of the corresponding output states [22]. Thus by combining the transformation induced by the q-plate and a polarizing beamsplitter the map φπ0oHπφo2 can be achieved with an efficiency of conversion equal to 50%. It is possible to realize a fully deterministic transferrer πo 2 at the price of a more complex optical layout, based on a q-plate and a Mach-Zehnder interferometer, as shown in [23]. After the transferrer operation the polarization entangled state is transformed into the hybrid entangled state:

12(HπA+2o2BVπA2o2B)0oAHπB
 

Fig. 3. Coincidence rate [DA,DB] measured as a function of the angle θ of the half wave plate on the arm kA for OAM detected state (a) ∣ + 2〉 and (b) ho2 .

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In order to analyze with high efficiency the OAM degree of freedom, we exploited the o 2π transferrer, as shown in [9, 23]. By this approach any measurement on the OAM state is achieved by measuring the polarization after the transferrer device, as shown in Fig. 1. Finally the photon has been coupled to a single mode fiber and then detected by DB connected to the coincidence box (CB), which records the coincidence counts between [DA,DB]. We observed a final coincidence rate equal to C = 100coinc/s within a coincidence window of 3 ns. This experimental data is in agreement with the expected value, determined from Csource = 6kHz after taking into account two main loss factors: hybrid state preparation probability pprep, and detection probability pdet. pprep depends on the conversion efficiency of the q-plate (0.80 ± 0.05) and on the probabilistic efficiency of the quantum transferrer πo 2 (0.5), thus leading to pprep = 0.40 ± 0.03. The detection efficiency includes the q-plate conversion efficiency (0.8), the transferrer o 2π (0.5), and the single mode fiber coupling (0.2). Hence pdet = 0.08. The observed experimental rate includes a reduction factor ~ 8 due to the adoption of probabilistic transferrers [23], and by achieving a higher single mode fiber coupling efficiency. Hence, by modifying the transferrers, we expect to achieve a detection rate equal to about 800coinc/s.

3. Characterization of the state

To completely characterize the state in Eq. 2 we reconstructed the density matrix of the quantum state. The tomography reconstruction requires the estimation of 16 operators [25] through 36 separable measurements on the polarization-OAM subspaces. We carried out the reconstruction of the density matrix ρπ,o2A,B after the polarization-OAM conversion. The experimental results are reported in Fig. 2, with the elements of the density matrices expressed in the polarization and OAM basis {∣H, + 2〉, ∣H, − 2〉, ∣V, + 2〉, ∣V, − 2〉}. The fidelity with the singlet states ∣Ψ 〉 has been evaluated to be F(Ψ,ρπ,o2A,B)=(0.957±0.009) , while the experimental linear entropy of the state reads SL = (0.012 ± 0.002). A more quantitative parameter associated to the generated polarization-entangled states is given by the concurrence C = (0.957 ± 0.002). These values demonstrate the high degree of hybrid entanglement generation.

To further characterize the hybrid quantum states, the violation of Bell’s inequalities with the two photon system have been addressed. First, we measured the photon coincidence rate as a function of the orientation of the half-wave plate on Alice arm for two different OAM basis analysis, namely {+2o2,2o2} and {ho2,vo2} . The variation of the number of coincidences N(θ) with the angle θ is in agreement with the one expected for entangled states such as N(θ) = N 0(1 + cosθ): Fig. 3. The coincidence fringe visibility reaches the values V = (0.966 ± 0.001) and V = (0.930 ± 0.007). Hence, a non-locality test, the CHSH one [26], has been carried out. Each of two partners, A (Alice) and B (Bob) measures a dichotomic observable among two possible ones, i.e. Alice randomly measures either a or a’ while Bob measures b or b’, where the outcomes of each measurement are either +1 or −1. For any couple of measured observables (A = {a, a’}, B = {b, b’}), we define the following correlation function E(A,B)=N(+,+)+N(,)N(+,)N(,+)N(+,+)+N(,)+N(+,)+N(,+) where N(i, j) stands for the number of events in which the observables A and B have been found equal to the dichotomic outcomes i and j. Finally we define the parameter S which takes into account the correlations for the different observables

S=E(a,b)+E(a,b)+E(a,b)E(a,b)

Assuming a local realistic theory, the relation ∣S∣ ≤ SCHSH = 2 holds. To carry out a non-locality test in the hybrid regime, we define the two sets of dichotomic observables for A and B. For Alice the basis a and a’ correspond, respectively, to the linear polarization basis {∣Hπ, ∣Vπ} and {∣ + 〉π, ∣ − 〉π}. For Bob the basis b and b’ correspond, respectively, to the OAM basis {cos(π8)+2sin(π8)2,sin(π8)+2+cos(π8)2} and {cos(π8)+2+sin(π8)2,sin(π8)+2cos(π8)2} . Experimentally we obtained the following value by carrying out a measurement with a duration of 60s and an average statistics per setting equal to about 1500 events: S = (2.51 ± 0.02). Hence a violation by more than 25 standard deviation over the value SCHSH = 2 is obtained. This experimental value is in good agreement with an experimental visibility of V = (0.930 ± 0.007) which should lead to S = (2.57 ± 0.02).

4. Conclusion

In conclusion, we presented a source of polarization-OAMhybrid entanglement based on SPDC source and πo 2 transferrer. We have shown that this system provides quantum states with high fidelity and with a bright generation rate. Moreover by adopting several concatenated q-plates the generation of hybrid states with higher OAM value could be obtained. Hybrid entangled states could be adopted to carry out quantum state teleportation between different degrees of freedom of light. Furthermore by inserting a quantum transferrer πo 2 also on mode kA, a controllable source of OAM entangled states could be achieved.

Acknowledgement

This work was supported by FARI project, Finanziamento Ateneo 2009 of Sapienza Universitá di Roma, project PHORBITECH of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission, under FET-Open grant number 255914, and project HYTEQ FIRB-Futuro in Ricerca (MIUR).

References and links

1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002). [CrossRef]  

2. F. De Martini and F. Sciarrino, “Non-linear parametric processes in quantum information,” Prog. Quantum Electron. 29, 165 (2005). [CrossRef]  

3. P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995). [CrossRef]   [PubMed]  

4. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773 (1999). [CrossRef]  

5. C. Cinelli, G. Di Nepi, F. De Martini, M. Barbieri, and P. Mataloni, “Parametric source of two-photon states with a tunable degree of entanglement and mixing: Experimental preparation of Werner states and maximally entangled mixed states,” Phys. Rev. A 70, 022321 (2004). [CrossRef]  

6. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305 (2007). [CrossRef]  

7. S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 4, 299313 (2008).

8. J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nature Phys. 4, 282 (2008). [CrossRef]  

9. E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence,” Nat. Photon. 3, 720 (2009). [CrossRef]  

10. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313 (2001). [CrossRef]   [PubMed]  

11. A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91, 227902 (2003). [CrossRef]   [PubMed]  

12. J. P. Torres, Y. Deyanova, and L. Torner, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003). [CrossRef]  

13. G. Molina-Terriza, A. Vaziri1, J. Rehcek, Z. Hradil, and A. Zeilinger, “Triggered Qutrits for Quantum Communication Protocols,” Phys. Rev. Lett. 92, 167903 (2004). [CrossRef]   [PubMed]  

14. N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment,” Phys. Rev. Lett. 93, 053601 (2004). [CrossRef]   [PubMed]  

15. G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental Quantum Coin Tossing,” Phys. Rev. Lett. 94, 040501 (2005). [CrossRef]   [PubMed]  

16. J. T. Barreiro, N. K. Langford, N. A. Peters, and P.G. Kwiat, “Generation of Hyperentangled photons pairs,” Phys. Rev. Lett. 95, 260501 (2005). [CrossRef]  

17. S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Elie, G. W. Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005). [CrossRef]   [PubMed]  

18. B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. OBrien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating Biphotonic Qutrits,” Phys. Rev. Lett. 100, 060504 (2008). [CrossRef]   [PubMed]  

19. X. Ma, A. Qarry, J.s Kofler, T. Jennewein, and A. Zeilinger, “Experimental violation of a Bell inequality with two different degrees of freedom of entangled particle pairs,” Phys. Rev. A 79, 042101 (2009). [CrossRef]  

20. L. Neves, G. Lima, A. Delgado, and C. Saavedra, “Hybrid photonic entanglement: Realization, characterization, and applications,” Phys. Rev. A 80, 042322 (2009). [CrossRef]  

21. L. Chen and W. She, “Teleportation of a controllable orbital angular momentum generator,” Phys. Rev. A 80, 063831 (2009). [CrossRef]  

22. E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009). [CrossRef]   [PubMed]  

23. E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17, 18745 (2009). [CrossRef]  

24. L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006). [CrossRef]   [PubMed]  

25. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001). [CrossRef]  

26. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880 (1969). [CrossRef]  

References

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  1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
    [CrossRef]
  2. F. De Martini, and F. Sciarrino, “Non-linear parametric processes in quantum information,” Prog. Quantum Electron. 29, 165 (2005).
    [CrossRef]
  3. P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
    [CrossRef] [PubMed]
  4. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarizationentangled photons,” Phys. Rev. A 60, R773 (1999).
    [CrossRef]
  5. C. Cinelli, G. Di Nepi, F. De Martini, M. Barbieri, and P. Mataloni, “Parametric source of two-photon states with a tunable degree of entanglement and mixing: Experimental preparation of Werner states and maximally entangled mixed states,” Phys. Rev. A 70, 022321 (2004).
    [CrossRef]
  6. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305 (2007).
    [CrossRef]
  7. S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 4, 299313 (2008).
  8. J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282 (2008).
    [CrossRef]
  9. E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720 (2009).
    [CrossRef]
  10. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313 (2001).
    [CrossRef] [PubMed]
  11. A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91, 227902 (2003).
    [CrossRef] [PubMed]
  12. J. P. Torres, Y. Deyanova, and L. Torner, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
    [CrossRef]
  13. G. Molina-Terriza, “A. Vaziri1, J. Rehcek, Z. Hradil, and A. Zeilinger, “Triggered Qutrits for Quantum Communication Protocols,” Phys. Rev. Lett. 92, 167903 (2004).
    [CrossRef] [PubMed]
  14. N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment,” Phys. Rev. Lett. 93, 053601 (2004).
    [CrossRef] [PubMed]
  15. G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental Quantum Coin Tossing,” Phys. Rev. Lett. 94, 040501 (2005).
    [CrossRef] [PubMed]
  16. J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of Hyperentangled photons pairs,” Phys. Rev. Lett. 95, 260501 (2005).
    [CrossRef]
  17. S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Elie, G. W. Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
    [CrossRef] [PubMed]
  18. B. P. Lanyon, T. J. Weinhold, and N. K. Langford, “J. L. OBrien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating Biphotonic Qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
    [CrossRef] [PubMed]
  19. X. Ma, and A. Qarry, “J.s Kofler, T.Jennewein, and A. Zeilinger, “Experimental violation of a Bell inequality with two different degrees of freedom of entangled particle pairs,” Phys. Rev. A 79, 042101 (2009).
    [CrossRef]
  20. L. Neves, G. Lima, A. Delgado, and C. Saavedra, “Hybrid photonic entanglement: Realization, characterization, and applications,” Phys. Rev. A 80, 042322 (2009).
    [CrossRef]
  21. L. Chen, and W. She, “Teleportation of a controllable orbital angular momentum generator,” Phys. Rev. A 80, 063831 (2009).
    [CrossRef]
  22. E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
    [CrossRef] [PubMed]
  23. E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17, 18745 (2009).
    [CrossRef]
  24. L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
    [CrossRef] [PubMed]
  25. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
    [CrossRef]
  26. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880 (1969).
    [CrossRef]

2009 (6)

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720 (2009).
[CrossRef]

X. Ma, and A. Qarry, “J.s Kofler, T.Jennewein, and A. Zeilinger, “Experimental violation of a Bell inequality with two different degrees of freedom of entangled particle pairs,” Phys. Rev. A 79, 042101 (2009).
[CrossRef]

L. Neves, G. Lima, A. Delgado, and C. Saavedra, “Hybrid photonic entanglement: Realization, characterization, and applications,” Phys. Rev. A 80, 042322 (2009).
[CrossRef]

L. Chen, and W. She, “Teleportation of a controllable orbital angular momentum generator,” Phys. Rev. A 80, 063831 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef] [PubMed]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17, 18745 (2009).
[CrossRef]

2008 (3)

B. P. Lanyon, T. J. Weinhold, and N. K. Langford, “J. L. OBrien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating Biphotonic Qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef] [PubMed]

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 4, 299313 (2008).

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282 (2008).
[CrossRef]

2007 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305 (2007).
[CrossRef]

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

2005 (4)

F. De Martini, and F. Sciarrino, “Non-linear parametric processes in quantum information,” Prog. Quantum Electron. 29, 165 (2005).
[CrossRef]

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental Quantum Coin Tossing,” Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of Hyperentangled photons pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Elie, G. W. Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

2004 (3)

G. Molina-Terriza, “A. Vaziri1, J. Rehcek, Z. Hradil, and A. Zeilinger, “Triggered Qutrits for Quantum Communication Protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef] [PubMed]

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

C. Cinelli, G. Di Nepi, F. De Martini, M. Barbieri, and P. Mataloni, “Parametric source of two-photon states with a tunable degree of entanglement and mixing: Experimental preparation of Werner states and maximally entangled mixed states,” Phys. Rev. A 70, 022321 (2004).
[CrossRef]

2003 (2)

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef] [PubMed]

J. P. Torres, Y. Deyanova, and L. Torner, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
[CrossRef]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

2001 (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313 (2001).
[CrossRef] [PubMed]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[CrossRef]

1999 (1)

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarizationentangled photons,” Phys. Rev. A 60, R773 (1999).
[CrossRef]

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

1969 (1)

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880 (1969).
[CrossRef]

Aiello, A.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Elie, G. W. Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 4, 299313 (2008).

Appelbaum, I.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarizationentangled photons,” Phys. Rev. A 60, R773 (1999).
[CrossRef]

Barbieri, M.

C. Cinelli, G. Di Nepi, F. De Martini, M. Barbieri, and P. Mataloni, “Parametric source of two-photon states with a tunable degree of entanglement and mixing: Experimental preparation of Werner states and maximally entangled mixed states,” Phys. Rev. A 70, 022321 (2004).
[CrossRef]

Barreiro, J. T.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282 (2008).
[CrossRef]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of Hyperentangled photons pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

Bartlett, S. D.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Chen, L.

L. Chen, and W. She, “Teleportation of a controllable orbital angular momentum generator,” Phys. Rev. A 80, 063831 (2009).
[CrossRef]

Cinelli, C.

C. Cinelli, G. Di Nepi, F. De Martini, M. Barbieri, and P. Mataloni, “Parametric source of two-photon states with a tunable degree of entanglement and mixing: Experimental preparation of Werner states and maximally entangled mixed states,” Phys. Rev. A 70, 022321 (2004).
[CrossRef]

Clauser, J. F.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880 (1969).
[CrossRef]

Dalton, R. B.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

De Martini, F.

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef] [PubMed]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17, 18745 (2009).
[CrossRef]

F. De Martini, and F. Sciarrino, “Non-linear parametric processes in quantum information,” Prog. Quantum Electron. 29, 165 (2005).
[CrossRef]

C. Cinelli, G. Di Nepi, F. De Martini, M. Barbieri, and P. Mataloni, “Parametric source of two-photon states with a tunable degree of entanglement and mixing: Experimental preparation of Werner states and maximally entangled mixed states,” Phys. Rev. A 70, 022321 (2004).
[CrossRef]

Delgado, A.

L. Neves, G. Lima, A. Delgado, and C. Saavedra, “Hybrid photonic entanglement: Realization, characterization, and applications,” Phys. Rev. A 80, 042322 (2009).
[CrossRef]

Deyanova, Y.

J. P. Torres, Y. Deyanova, and L. Torner, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
[CrossRef]

Di Nepi, G.

C. Cinelli, G. Di Nepi, F. De Martini, M. Barbieri, and P. Mataloni, “Parametric source of two-photon states with a tunable degree of entanglement and mixing: Experimental preparation of Werner states and maximally entangled mixed states,” Phys. Rev. A 70, 022321 (2004).
[CrossRef]

Eberhard, P. H.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarizationentangled photons,” Phys. Rev. A 60, R773 (1999).
[CrossRef]

Elie, E. R.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Elie, G. W. Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

Franke-Arnold, S.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 4, 299313 (2008).

Gilchrist, A.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Harvey, M. D.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Holt, R. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880 (1969).
[CrossRef]

Hooft, G. W.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Elie, G. W. Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

Horne, M. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880 (1969).
[CrossRef]

James, D. F. V.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[CrossRef]

Jennewein, T.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef] [PubMed]

Karimi, E.

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17, 18745 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef] [PubMed]

Kwiat, P. G.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282 (2008).
[CrossRef]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of Hyperentangled photons pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[CrossRef]

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarizationentangled photons,” Phys. Rev. A 60, R773 (1999).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Langford, N. K.

B. P. Lanyon, T. J. Weinhold, and N. K. Langford, “J. L. OBrien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating Biphotonic Qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef] [PubMed]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of Hyperentangled photons pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Lanyon, B. P.

B. P. Lanyon, T. J. Weinhold, and N. K. Langford, “J. L. OBrien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating Biphotonic Qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef] [PubMed]

Lima, G.

L. Neves, G. Lima, A. Delgado, and C. Saavedra, “Hybrid photonic entanglement: Realization, characterization, and applications,” Phys. Rev. A 80, 042322 (2009).
[CrossRef]

Ma, X.

X. Ma, and A. Qarry, “J.s Kofler, T.Jennewein, and A. Zeilinger, “Experimental violation of a Bell inequality with two different degrees of freedom of entangled particle pairs,” Phys. Rev. A 79, 042101 (2009).
[CrossRef]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Elie, G. W. Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313 (2001).
[CrossRef] [PubMed]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

Marrucci, L.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef] [PubMed]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17, 18745 (2009).
[CrossRef]

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720 (2009).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

Mataloni, P.

C. Cinelli, G. Di Nepi, F. De Martini, M. Barbieri, and P. Mataloni, “Parametric source of two-photon states with a tunable degree of entanglement and mixing: Experimental preparation of Werner states and maximally entangled mixed states,” Phys. Rev. A 70, 022321 (2004).
[CrossRef]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305 (2007).
[CrossRef]

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental Quantum Coin Tossing,” Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

G. Molina-Terriza, “A. Vaziri1, J. Rehcek, Z. Hradil, and A. Zeilinger, “Triggered Qutrits for Quantum Communication Protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef] [PubMed]

Munro, W. J.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[CrossRef]

Nagali, E.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17, 18745 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef] [PubMed]

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720 (2009).
[CrossRef]

Neves, L.

L. Neves, G. Lima, A. Delgado, and C. Saavedra, “Hybrid photonic entanglement: Realization, characterization, and applications,” Phys. Rev. A 80, 042322 (2009).
[CrossRef]

O’Brien, J. L.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Oemrawsingh, S. S. R.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Elie, G. W. Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

Padgett, M.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 4, 299313 (2008).

Pan, J. W.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef] [PubMed]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

Peters, N. A.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of Hyperentangled photons pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

Piccirillo, B.

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17, 18745 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef] [PubMed]

Pryde, G. J.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Qarry, A.

X. Ma, and A. Qarry, “J.s Kofler, T.Jennewein, and A. Zeilinger, “Experimental violation of a Bell inequality with two different degrees of freedom of entangled particle pairs,” Phys. Rev. A 79, 042101 (2009).
[CrossRef]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Saavedra, C.

L. Neves, G. Lima, A. Delgado, and C. Saavedra, “Hybrid photonic entanglement: Realization, characterization, and applications,” Phys. Rev. A 80, 042322 (2009).
[CrossRef]

Sansoni, L.

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720 (2009).
[CrossRef]

Santamato, E.

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef] [PubMed]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17, 18745 (2009).
[CrossRef]

Sciarrino, F.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17, 18745 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef] [PubMed]

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720 (2009).
[CrossRef]

F. De Martini, and F. Sciarrino, “Non-linear parametric processes in quantum information,” Prog. Quantum Electron. 29, 165 (2005).
[CrossRef]

She, W.

L. Chen, and W. She, “Teleportation of a controllable orbital angular momentum generator,” Phys. Rev. A 80, 063831 (2009).
[CrossRef]

Shimony, A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880 (1969).
[CrossRef]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305 (2007).
[CrossRef]

J. P. Torres, Y. Deyanova, and L. Torner, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305 (2007).
[CrossRef]

J. P. Torres, Y. Deyanova, and L. Torner, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
[CrossRef]

Ursin, R.

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental Quantum Coin Tossing,” Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

Vaziri, A.

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental Quantum Coin Tossing,” Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313 (2001).
[CrossRef] [PubMed]

Voigt, D.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Elie, G. W. Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

Waks, E.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarizationentangled photons,” Phys. Rev. A 60, R773 (1999).
[CrossRef]

Wei, T. C.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282 (2008).
[CrossRef]

Weihs, G.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313 (2001).
[CrossRef] [PubMed]

Weinfurter, H.

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Weinhold, T. J.

B. P. Lanyon, T. J. Weinhold, and N. K. Langford, “J. L. OBrien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating Biphotonic Qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef] [PubMed]

White, A. G.

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[CrossRef]

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarizationentangled photons,” Phys. Rev. A 60, R773 (1999).
[CrossRef]

Woerdman, J. P.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Elie, G. W. Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Zeilinger, A.

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental Quantum Coin Tossing,” Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313 (2001).
[CrossRef] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Laser Photonics Rev. (1)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 4, 299313 (2008).

Nat. Photonics (1)

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence,” Nat. Photonics 3, 720 (2009).
[CrossRef]

Nat. Phys. (2)

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282 (2008).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305 (2007).
[CrossRef]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313 (2001).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. A (7)

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[CrossRef]

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarizationentangled photons,” Phys. Rev. A 60, R773 (1999).
[CrossRef]

C. Cinelli, G. Di Nepi, F. De Martini, M. Barbieri, and P. Mataloni, “Parametric source of two-photon states with a tunable degree of entanglement and mixing: Experimental preparation of Werner states and maximally entangled mixed states,” Phys. Rev. A 70, 022321 (2004).
[CrossRef]

J. P. Torres, Y. Deyanova, and L. Torner, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
[CrossRef]

X. Ma, and A. Qarry, “J.s Kofler, T.Jennewein, and A. Zeilinger, “Experimental violation of a Bell inequality with two different degrees of freedom of entangled particle pairs,” Phys. Rev. A 79, 042101 (2009).
[CrossRef]

L. Neves, G. Lima, A. Delgado, and C. Saavedra, “Hybrid photonic entanglement: Realization, characterization, and applications,” Phys. Rev. A 80, 042322 (2009).
[CrossRef]

L. Chen, and W. She, “Teleportation of a controllable orbital angular momentum generator,” Phys. Rev. A 80, 063831 (2009).
[CrossRef]

Phys. Rev. Lett. (11)

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef] [PubMed]

G. Molina-Terriza, “A. Vaziri1, J. Rehcek, Z. Hradil, and A. Zeilinger, “Triggered Qutrits for Quantum Communication Protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef] [PubMed]

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental Quantum Coin Tossing,” Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of Hyperentangled photons pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Elie, G. W. Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

B. P. Lanyon, T. J. Weinhold, and N. K. Langford, “J. L. OBrien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating Biphotonic Qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880 (1969).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91, 227902 (2003).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

F. De Martini, and F. Sciarrino, “Non-linear parametric processes in quantum information,” Prog. Quantum Electron. 29, 165 (2005).
[CrossRef]

Rev. Mod. Phys. (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Experimental setup adopted for the generation and characterization of hybrid π-OAM entangled states.(A)Generation of polarization entangled photons on modes kA and kB .(B)Projection on the OAM state with m = 0 through the coupling on a single mode fiber (SMF).(C)Encoding of the state in the OAM subspace o 2 through the πo 2 transferrer.

Fig. 2.
Fig. 2.

Experimental density matrix of the hybrid entangled state generated after the transferrer transformation on photons on kB mode. Each measurement setting lasted 15s.

Fig. 3.
Fig. 3.

Coincidence rate [DA ,DB ] measured as a function of the angle θ of the half wave plate on the arm kA for OAM detected state (a) ∣ + 2〉 and (b) h o 2 .

Equations (4)

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

L π 0 o QP R π + 2 o 2
R π 0 o QP L π 2 o 2
1 2 ( H π A + 2 o 2 B V π A 2 o 2 B ) 0 o A H π B
S = E ( a , b ) + E ( a , b ) + E ( a , b ) E ( a , b )

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