Abstract

We investigate the statistical properties and inseparability of the field states generated by any order nonlocal coherent photon addition (CPA) to the two-mode squeezed vacuum (TMSV). It is shown that the normalization factor of the CPA-TMSV is a Legendre polynomial, a compact expression. The statistical properties are discussed according to the analytical expressions of cross-correlation function, antibunching effect, and the negativity of its Wigner function. The inseparability is presented by using Shchukin–Vogel criteria and the Einstein–Podolsky–Rosen correlation. It is found that the symmetrical CPA-TMSV may possess stronger correlation than the single-mode photon-addition case. The lower bound of entanglement of the CPA-TMSV is considered, which indicates the logarithmic negativity is invalid for verifying the entanglement when the squeezing parameter is less than a threshold value, a period function of π/2. In addition, quantum teleportation is examined, which shows that asymmetric photon-added TMSV may be more useful for teleportation than the symmetric case.

© 2013 Optical Society of America

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  3. G. Giedke, and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002).
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  4. J. Fiurasek, “Gaussian transformations and distillation of entangled Gaussian states,” Phys. Rev. Lett. 89, 137904 (2002).
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  5. A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
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  6. A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
    [CrossRef]
  7. V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
    [CrossRef]
  8. M. S. Kim, “Recent developments in photon-level operations on travelling light fields,” J. Phys. B 41, 133001 (2008).
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  9. G. S. Agarwal, and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492–497 (1991).
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  10. L. Y. Hu, and Z. M. Zhang, “Nonclassicality and decoherence of photon-added squeezed thermal state in thermal environment,” J. Opt. Soc. Am. B 29, 529–537 (2012).
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  11. A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73, 042310 (2006).
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  14. H. Nha, and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
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  15. R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Proposal for a loophole-free Bell test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
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  16. S. D. Bartlett, and B. C. Sanders, “Universal continuous-variable quantum computation: requirement of optical nonlinearity for photon counting,” Phys. Rev. A 65, 042304 (2002).
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  17. S. Zhang, and P. van Loock, “Local Gaussian operations can enhance continuous-variable entanglement distillation,” Phys. Rev. A 84, 062309 (2011).
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  18. J. Fiurasek, “Improving entanglement concentration of Gaussian states by local displacements,” Phys. Rev. A 84, 012335 (2011).
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  26. J. Fiurasek, “Conditional generation of N-photon entangled states of light,” Phys. Rev. A 65, 053818 (2002).
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  27. P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A 65, 052104 (2002).
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  28. S. Y. Lee and H. Nha, “Second-order superposition operations via Hong–Ou–Mandel interference,” Phys. Rev. A 85, 043816 (2012).
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  29. G. S. Agarwal, R. R. Puri, and R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207–4215 (1997).
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  30. A. Zavatta, J. Fiurasek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52–60 (2010).
    [CrossRef]
  31. A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).
    [CrossRef]
  32. L.-Y. Hu and Z.-M. Zhang, “Entanglement and nonclassicality of photon-added two-mode squeezed thermal state,” J. Opt. Soc. Am. B 29, 1456–1464 (2012).
    [CrossRef]
  33. C. T. Lee, “Many-photon anti-bunching in generalized pair coherent states,” Phys. Rev. A 41, 1569–1575 (1990).
    [CrossRef]
  34. L. Y. Hu, X. X. Xu, and H. Y. Fan, “Statistical properties of photon-subtracted two-mode squeezed vacuum and its decoherence in thermal environment,” J. Opt. Soc. Am. B 27, 286–299 (2010).
    [CrossRef]
  35. H. Y. Fan and H. R. Zaidi, “Application of IWOP technique to the generalized Weyl correspondence,” Phys. Lett. A 124, 303–307 (1987).
    [CrossRef]
  36. E. Shchukin and W. Vogel, “Inseparability criteria for continuous bipartite quantum states,” Phys. Rev. Lett. 95, 230502 (2005).
    [CrossRef]
  37. L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
    [CrossRef]
  38. R. Simon, “Peres–Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
    [CrossRef]
  39. M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of Gaussian quantum states,” Phys. Rev. Lett. 96, 080502 (2006).
    [CrossRef]
  40. H. R. Li, F. L. Li, and S. Y. Zhu, “Inseparability of photon-added Gaussian states,” Phys. Rev. A 75, 062318 (2007).
    [CrossRef]
  41. A. Serafini, F. Illuminati, M. G. A. Paris, and S. De Siena, “Entanglement and purity of two-mode Gaussian states in noisy channels,” Phys. Rev. A 69, 022318 (2004).
    [CrossRef]
  42. G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
    [CrossRef]
  43. G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
    [CrossRef]
  44. P. Marian and T. A. Marian, “Continuous-variable teleportation in the characteristic-function description,” Phys. Rev. A 74, 042306 (2006).
    [CrossRef]
  45. S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
    [CrossRef]
  46. L.-Y. Hu and H.-Y. Fan, “Statistical properties of photon-subtracted squeezed vacuum in thermal environment,” J. Opt. Soc. Am. B 25, 1955–1964 (2008).
    [CrossRef]
  47. L. Z. Jiang, X. Y. Chen, T. Y. Ye, and F. Y. Hong, “Entanglement criterion for coherent subtraction and coherent addition bipartite continuous variable states,” arXiv:1211.5826.

2012 (4)

L. Y. Hu, and Z. M. Zhang, “Nonclassicality and decoherence of photon-added squeezed thermal state in thermal environment,” J. Opt. Soc. Am. B 29, 529–537 (2012).
[CrossRef]

H. J. Kim, S. Y. Lee, S. W. Ji, and H. Nha, “Quantum linear amplifier enhanced by photon subtraction and addition,” Phys. Rev. A 85, 013839 (2012).
[CrossRef]

S. Y. Lee and H. Nha, “Second-order superposition operations via Hong–Ou–Mandel interference,” Phys. Rev. A 85, 043816 (2012).
[CrossRef]

L.-Y. Hu and Z.-M. Zhang, “Entanglement and nonclassicality of photon-added two-mode squeezed thermal state,” J. Opt. Soc. Am. B 29, 1456–1464 (2012).
[CrossRef]

2011 (4)

S. Y. Lee, S. W. Ji, H. J. Kim, and H. Nha, “Enhancing quantum entanglement for continuous variables by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 84, 012302 (2011).
[CrossRef]

J. Jeffers, “Optical amplifier-powered quantum optical amplification,” Phys. Rev. A 83, 053818 (2011).
[CrossRef]

S. Zhang, and P. van Loock, “Local Gaussian operations can enhance continuous-variable entanglement distillation,” Phys. Rev. A 84, 062309 (2011).
[CrossRef]

J. Fiurasek, “Improving entanglement concentration of Gaussian states by local displacements,” Phys. Rev. A 84, 012335 (2011).
[CrossRef]

2010 (4)

J. Fiurasek, “Distillation and purification of symmetric entangled Gaussian states,” Phys. Rev. A 82, 042331 (2010).
[CrossRef]

S. Y. Lee, and H. Nha, “Quantum state engineering by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 82, 053812 (2010).
[CrossRef]

A. Zavatta, J. Fiurasek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52–60 (2010).
[CrossRef]

L. Y. Hu, X. X. Xu, and H. Y. Fan, “Statistical properties of photon-subtracted two-mode squeezed vacuum and its decoherence in thermal environment,” J. Opt. Soc. Am. B 27, 286–299 (2010).
[CrossRef]

2009 (2)

A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).
[CrossRef]

Y. Yang, and F. L. Li, “Entanglement properties of non-Gaussian resources generated via photon subtraction and addition and continuous-variable quantum-teleportation improvement,” Phys. Rev. A 80, 022315 (2009).
[CrossRef]

2008 (2)

M. S. Kim, “Recent developments in photon-level operations on travelling light fields,” J. Phys. B 41, 133001 (2008).
[CrossRef]

L.-Y. Hu and H.-Y. Fan, “Statistical properties of photon-subtracted squeezed vacuum in thermal environment,” J. Opt. Soc. Am. B 25, 1955–1964 (2008).
[CrossRef]

2007 (4)

H. R. Li, F. L. Li, and S. Y. Zhu, “Inseparability of photon-added Gaussian states,” Phys. Rev. A 75, 062318 (2007).
[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
[CrossRef]

2006 (4)

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73, 042310 (2006).
[CrossRef]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[CrossRef]

M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of Gaussian quantum states,” Phys. Rev. Lett. 96, 080502 (2006).
[CrossRef]

P. Marian and T. A. Marian, “Continuous-variable teleportation in the characteristic-function description,” Phys. Rev. A 74, 042306 (2006).
[CrossRef]

2005 (1)

E. Shchukin and W. Vogel, “Inseparability criteria for continuous bipartite quantum states,” Phys. Rev. Lett. 95, 230502 (2005).
[CrossRef]

2004 (5)

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[CrossRef]

H. Nha, and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Proposal for a loophole-free Bell test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
[CrossRef]

A. Serafini, F. Illuminati, M. G. A. Paris, and S. De Siena, “Entanglement and purity of two-mode Gaussian states in noisy channels,” Phys. Rev. A 69, 022318 (2004).
[CrossRef]

2003 (1)

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

2002 (7)

S. D. Bartlett, and B. C. Sanders, “Universal continuous-variable quantum computation: requirement of optical nonlinearity for photon counting,” Phys. Rev. A 65, 042304 (2002).
[CrossRef]

J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
[CrossRef]

G. Giedke, and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002).
[CrossRef]

J. Fiurasek, “Gaussian transformations and distillation of entangled Gaussian states,” Phys. Rev. Lett. 89, 137904 (2002).
[CrossRef]

J. Fiurasek, “Conditional generation of N-photon entangled states of light,” Phys. Rev. A 65, 053818 (2002).
[CrossRef]

P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A 65, 052104 (2002).
[CrossRef]

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[CrossRef]

2000 (2)

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

R. Simon, “Peres–Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
[CrossRef]

1998 (1)

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

1997 (1)

G. S. Agarwal, R. R. Puri, and R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207–4215 (1997).
[CrossRef]

1991 (1)

G. S. Agarwal, and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492–497 (1991).
[CrossRef]

1990 (1)

C. T. Lee, “Many-photon anti-bunching in generalized pair coherent states,” Phys. Rev. A 41, 1569–1575 (1990).
[CrossRef]

1987 (1)

H. Y. Fan and H. R. Zaidi, “Application of IWOP technique to the generalized Weyl correspondence,” Phys. Lett. A 124, 303–307 (1987).
[CrossRef]

Adesso, G.

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, R. R. Puri, and R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207–4215 (1997).
[CrossRef]

G. S. Agarwal, and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492–497 (1991).
[CrossRef]

Bartlett, S. D.

S. D. Bartlett, and B. C. Sanders, “Universal continuous-variable quantum computation: requirement of optical nonlinearity for photon counting,” Phys. Rev. A 65, 042304 (2002).
[CrossRef]

Bellini, M.

A. Zavatta, J. Fiurasek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52–60 (2010).
[CrossRef]

A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).
[CrossRef]

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[CrossRef]

Bouwmeester, D.

D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer-Verlag, 2000).

Braunstein, S. L.

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

Browne, D. E.

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

Carmichael, H. J.

H. Nha, and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
[CrossRef]

Cerf, N. J.

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Proposal for a loophole-free Bell test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

Chefles, A.

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73, 042310 (2006).
[CrossRef]

Chen, X. Y.

L. Z. Jiang, X. Y. Chen, T. Y. Ye, and F. Y. Hong, “Entanglement criterion for coherent subtraction and coherent addition bipartite continuous variable states,” arXiv:1211.5826.

Cirac, J. I.

M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of Gaussian quantum states,” Phys. Rev. Lett. 96, 080502 (2006).
[CrossRef]

G. Giedke, and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002).
[CrossRef]

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

Dantan, A.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

De Siena, S.

A. Serafini, F. Illuminati, M. G. A. Paris, and S. De Siena, “Entanglement and purity of two-mode Gaussian states in noisy channels,” Phys. Rev. A 69, 022318 (2004).
[CrossRef]

Dowling, J. P.

P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A 65, 052104 (2002).
[CrossRef]

Duan, L. M.

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

Eisert, J.

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
[CrossRef]

Ekert, A.

D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer-Verlag, 2000).

Fan, H. Y.

Fan, H.-Y.

Fiurasek, J.

J. Fiurasek, “Improving entanglement concentration of Gaussian states by local displacements,” Phys. Rev. A 84, 012335 (2011).
[CrossRef]

J. Fiurasek, “Distillation and purification of symmetric entangled Gaussian states,” Phys. Rev. A 82, 042331 (2010).
[CrossRef]

A. Zavatta, J. Fiurasek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52–60 (2010).
[CrossRef]

J. Fiurasek, “Conditional generation of N-photon entangled states of light,” Phys. Rev. A 65, 053818 (2002).
[CrossRef]

J. Fiurasek, “Gaussian transformations and distillation of entangled Gaussian states,” Phys. Rev. Lett. 89, 137904 (2002).
[CrossRef]

Fiurášek, J.

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Proposal for a loophole-free Bell test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

García-Patrón, R.

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Proposal for a loophole-free Bell test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

Giedke, G.

M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of Gaussian quantum states,” Phys. Rev. Lett. 96, 080502 (2006).
[CrossRef]

G. Giedke, and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002).
[CrossRef]

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

Grangier, P.

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Proposal for a loophole-free Bell test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

Grangier, Ph.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

Hong, F. Y.

L. Z. Jiang, X. Y. Chen, T. Y. Ye, and F. Y. Hong, “Entanglement criterion for coherent subtraction and coherent addition bipartite continuous variable states,” arXiv:1211.5826.

Hu, L. Y.

Hu, L.-Y.

Illuminati, F.

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
[CrossRef]

A. Serafini, F. Illuminati, M. G. A. Paris, and S. De Siena, “Entanglement and purity of two-mode Gaussian states in noisy channels,” Phys. Rev. A 69, 022318 (2004).
[CrossRef]

Jeffers, J.

J. Jeffers, “Optical amplifier-powered quantum optical amplification,” Phys. Rev. A 83, 053818 (2011).
[CrossRef]

Jeong, H.

A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).
[CrossRef]

Ji, S. W.

H. J. Kim, S. Y. Lee, S. W. Ji, and H. Nha, “Quantum linear amplifier enhanced by photon subtraction and addition,” Phys. Rev. A 85, 013839 (2012).
[CrossRef]

S. Y. Lee, S. W. Ji, H. J. Kim, and H. Nha, “Enhancing quantum entanglement for continuous variables by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 84, 012302 (2011).
[CrossRef]

Jiang, L. Z.

L. Z. Jiang, X. Y. Chen, T. Y. Ye, and F. Y. Hong, “Entanglement criterion for coherent subtraction and coherent addition bipartite continuous variable states,” arXiv:1211.5826.

Kim, H. J.

H. J. Kim, S. Y. Lee, S. W. Ji, and H. Nha, “Quantum linear amplifier enhanced by photon subtraction and addition,” Phys. Rev. A 85, 013839 (2012).
[CrossRef]

S. Y. Lee, S. W. Ji, H. J. Kim, and H. Nha, “Enhancing quantum entanglement for continuous variables by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 84, 012302 (2011).
[CrossRef]

Kim, M.

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
[CrossRef]

Kim, M. S.

A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).
[CrossRef]

M. S. Kim, “Recent developments in photon-level operations on travelling light fields,” J. Phys. B 41, 133001 (2008).
[CrossRef]

Kimble, H. J.

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

Kitagawa, A.

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73, 042310 (2006).
[CrossRef]

Kok, P.

P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A 65, 052104 (2002).
[CrossRef]

Laurat, J.

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[CrossRef]

Lee, C. T.

C. T. Lee, “Many-photon anti-bunching in generalized pair coherent states,” Phys. Rev. A 41, 1569–1575 (1990).
[CrossRef]

Lee, H.

P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A 65, 052104 (2002).
[CrossRef]

Lee, S. Y.

S. Y. Lee and H. Nha, “Second-order superposition operations via Hong–Ou–Mandel interference,” Phys. Rev. A 85, 043816 (2012).
[CrossRef]

H. J. Kim, S. Y. Lee, S. W. Ji, and H. Nha, “Quantum linear amplifier enhanced by photon subtraction and addition,” Phys. Rev. A 85, 013839 (2012).
[CrossRef]

S. Y. Lee, S. W. Ji, H. J. Kim, and H. Nha, “Enhancing quantum entanglement for continuous variables by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 84, 012302 (2011).
[CrossRef]

S. Y. Lee, and H. Nha, “Quantum state engineering by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 82, 053812 (2010).
[CrossRef]

Li, F. L.

Y. Yang, and F. L. Li, “Entanglement properties of non-Gaussian resources generated via photon subtraction and addition and continuous-variable quantum-teleportation improvement,” Phys. Rev. A 80, 022315 (2009).
[CrossRef]

H. R. Li, F. L. Li, and S. Y. Zhu, “Inseparability of photon-added Gaussian states,” Phys. Rev. A 75, 062318 (2007).
[CrossRef]

Li, H. R.

H. R. Li, F. L. Li, and S. Y. Zhu, “Inseparability of photon-added Gaussian states,” Phys. Rev. A 75, 062318 (2007).
[CrossRef]

Marian, P.

P. Marian and T. A. Marian, “Continuous-variable teleportation in the characteristic-function description,” Phys. Rev. A 74, 042306 (2006).
[CrossRef]

Marian, T. A.

P. Marian and T. A. Marian, “Continuous-variable teleportation in the characteristic-function description,” Phys. Rev. A 74, 042306 (2006).
[CrossRef]

Nha, H.

S. Y. Lee and H. Nha, “Second-order superposition operations via Hong–Ou–Mandel interference,” Phys. Rev. A 85, 043816 (2012).
[CrossRef]

H. J. Kim, S. Y. Lee, S. W. Ji, and H. Nha, “Quantum linear amplifier enhanced by photon subtraction and addition,” Phys. Rev. A 85, 013839 (2012).
[CrossRef]

S. Y. Lee, S. W. Ji, H. J. Kim, and H. Nha, “Enhancing quantum entanglement for continuous variables by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 84, 012302 (2011).
[CrossRef]

S. Y. Lee, and H. Nha, “Quantum state engineering by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 82, 053812 (2010).
[CrossRef]

H. Nha, and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
[CrossRef]

Ourjoumtsev, A.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[CrossRef]

Parigi, V.

A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).
[CrossRef]

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
[CrossRef]

Paris, M. G. A.

A. Serafini, F. Illuminati, M. G. A. Paris, and S. De Siena, “Entanglement and purity of two-mode Gaussian states in noisy channels,” Phys. Rev. A 69, 022318 (2004).
[CrossRef]

Plenio, M. B.

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
[CrossRef]

Puri, R. R.

G. S. Agarwal, R. R. Puri, and R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207–4215 (1997).
[CrossRef]

Sanders, B. C.

S. D. Bartlett, and B. C. Sanders, “Universal continuous-variable quantum computation: requirement of optical nonlinearity for photon counting,” Phys. Rev. A 65, 042304 (2002).
[CrossRef]

Sasaki, M.

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73, 042310 (2006).
[CrossRef]

Scheel, S.

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
[CrossRef]

Serafini, A.

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
[CrossRef]

A. Serafini, F. Illuminati, M. G. A. Paris, and S. De Siena, “Entanglement and purity of two-mode Gaussian states in noisy channels,” Phys. Rev. A 69, 022318 (2004).
[CrossRef]

Shchukin, E.

E. Shchukin and W. Vogel, “Inseparability criteria for continuous bipartite quantum states,” Phys. Rev. Lett. 95, 230502 (2005).
[CrossRef]

Simon, R.

R. Simon, “Peres–Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
[CrossRef]

Singh, R. P.

G. S. Agarwal, R. R. Puri, and R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207–4215 (1997).
[CrossRef]

Takeoka, M.

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73, 042310 (2006).
[CrossRef]

Tara, K.

G. S. Agarwal, and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492–497 (1991).
[CrossRef]

Tualle-Brouri, R.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Proposal for a loophole-free Bell test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

van Loock, P.

S. Zhang, and P. van Loock, “Local Gaussian operations can enhance continuous-variable entanglement distillation,” Phys. Rev. A 84, 062309 (2011).
[CrossRef]

Viciani, S.

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[CrossRef]

Vidal, G.

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[CrossRef]

Vogel, W.

E. Shchukin and W. Vogel, “Inseparability criteria for continuous bipartite quantum states,” Phys. Rev. Lett. 95, 230502 (2005).
[CrossRef]

Wenger, J.

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Proposal for a loophole-free Bell test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

Werner, R. F.

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[CrossRef]

Wolf, M. M.

M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of Gaussian quantum states,” Phys. Rev. Lett. 96, 080502 (2006).
[CrossRef]

Xu, X. X.

Yang, Y.

Y. Yang, and F. L. Li, “Entanglement properties of non-Gaussian resources generated via photon subtraction and addition and continuous-variable quantum-teleportation improvement,” Phys. Rev. A 80, 022315 (2009).
[CrossRef]

Ye, T. Y.

L. Z. Jiang, X. Y. Chen, T. Y. Ye, and F. Y. Hong, “Entanglement criterion for coherent subtraction and coherent addition bipartite continuous variable states,” arXiv:1211.5826.

Zaidi, H. R.

H. Y. Fan and H. R. Zaidi, “Application of IWOP technique to the generalized Weyl correspondence,” Phys. Lett. A 124, 303–307 (1987).
[CrossRef]

Zavatta, A.

A. Zavatta, J. Fiurasek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52–60 (2010).
[CrossRef]

A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).
[CrossRef]

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[CrossRef]

Zeilinger, A.

D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer-Verlag, 2000).

Zhang, S.

S. Zhang, and P. van Loock, “Local Gaussian operations can enhance continuous-variable entanglement distillation,” Phys. Rev. A 84, 062309 (2011).
[CrossRef]

Zhang, Z. M.

Zhang, Z.-M.

Zhu, S. Y.

H. R. Li, F. L. Li, and S. Y. Zhu, “Inseparability of photon-added Gaussian states,” Phys. Rev. A 75, 062318 (2007).
[CrossRef]

Zoller, P.

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Phys. B (1)

M. S. Kim, “Recent developments in photon-level operations on travelling light fields,” J. Phys. B 41, 133001 (2008).
[CrossRef]

Nat. Photonics (1)

A. Zavatta, J. Fiurasek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52–60 (2010).
[CrossRef]

Phys. Lett. A (1)

H. Y. Fan and H. R. Zaidi, “Application of IWOP technique to the generalized Weyl correspondence,” Phys. Lett. A 124, 303–307 (1987).
[CrossRef]

Phys. Rev. A (23)

C. T. Lee, “Many-photon anti-bunching in generalized pair coherent states,” Phys. Rev. A 41, 1569–1575 (1990).
[CrossRef]

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73, 042310 (2006).
[CrossRef]

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

J. Fiurasek, “Conditional generation of N-photon entangled states of light,” Phys. Rev. A 65, 053818 (2002).
[CrossRef]

P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A 65, 052104 (2002).
[CrossRef]

S. Y. Lee and H. Nha, “Second-order superposition operations via Hong–Ou–Mandel interference,” Phys. Rev. A 85, 043816 (2012).
[CrossRef]

G. S. Agarwal, R. R. Puri, and R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207–4215 (1997).
[CrossRef]

G. S. Agarwal, and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492–497 (1991).
[CrossRef]

G. Giedke, and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002).
[CrossRef]

S. D. Bartlett, and B. C. Sanders, “Universal continuous-variable quantum computation: requirement of optical nonlinearity for photon counting,” Phys. Rev. A 65, 042304 (2002).
[CrossRef]

S. Zhang, and P. van Loock, “Local Gaussian operations can enhance continuous-variable entanglement distillation,” Phys. Rev. A 84, 062309 (2011).
[CrossRef]

J. Fiurasek, “Improving entanglement concentration of Gaussian states by local displacements,” Phys. Rev. A 84, 012335 (2011).
[CrossRef]

Y. Yang, and F. L. Li, “Entanglement properties of non-Gaussian resources generated via photon subtraction and addition and continuous-variable quantum-teleportation improvement,” Phys. Rev. A 80, 022315 (2009).
[CrossRef]

J. Fiurasek, “Distillation and purification of symmetric entangled Gaussian states,” Phys. Rev. A 82, 042331 (2010).
[CrossRef]

S. Y. Lee, and H. Nha, “Quantum state engineering by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 82, 053812 (2010).
[CrossRef]

S. Y. Lee, S. W. Ji, H. J. Kim, and H. Nha, “Enhancing quantum entanglement for continuous variables by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 84, 012302 (2011).
[CrossRef]

H. J. Kim, S. Y. Lee, S. W. Ji, and H. Nha, “Quantum linear amplifier enhanced by photon subtraction and addition,” Phys. Rev. A 85, 013839 (2012).
[CrossRef]

J. Jeffers, “Optical amplifier-powered quantum optical amplification,” Phys. Rev. A 83, 053818 (2011).
[CrossRef]

H. R. Li, F. L. Li, and S. Y. Zhu, “Inseparability of photon-added Gaussian states,” Phys. Rev. A 75, 062318 (2007).
[CrossRef]

A. Serafini, F. Illuminati, M. G. A. Paris, and S. De Siena, “Entanglement and purity of two-mode Gaussian states in noisy channels,” Phys. Rev. A 69, 022318 (2004).
[CrossRef]

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[CrossRef]

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
[CrossRef]

P. Marian and T. A. Marian, “Continuous-variable teleportation in the characteristic-function description,” Phys. Rev. A 74, 042306 (2006).
[CrossRef]

Phys. Rev. Lett. (12)

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

J. Fiurasek, “Gaussian transformations and distillation of entangled Gaussian states,” Phys. Rev. Lett. 89, 137904 (2002).
[CrossRef]

J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
[CrossRef]

H. Nha, and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Proposal for a loophole-free Bell test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).
[CrossRef]

E. Shchukin and W. Vogel, “Inseparability criteria for continuous bipartite quantum states,” Phys. Rev. Lett. 95, 230502 (2005).
[CrossRef]

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

R. Simon, “Peres–Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
[CrossRef]

M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of Gaussian quantum states,” Phys. Rev. Lett. 96, 080502 (2006).
[CrossRef]

Science (3)

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[CrossRef]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[CrossRef]

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
[CrossRef]

Other (2)

D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer-Verlag, 2000).

L. Z. Jiang, X. Y. Chen, T. Y. Ye, and F. Y. Hong, “Entanglement criterion for coherent subtraction and coherent addition bipartite continuous variable states,” arXiv:1211.5826.

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Figures (9)

Fig. 1.
Fig. 1.

gm as a function of φ and r for different parameters m. (a) m=0, (b) m=1, (c) m=2, and (d) m=3.

Fig. 2.
Fig. 2.

Rab as a function of φ and r for different parameters m. (a) m=2, (b) m=3, (c) m=0, 1, and m=2, 3 with φ=0, π/4.

Fig. 3.
Fig. 3.

WF W(α,β) in phase space for several different parameter values m with r=0.3 and φ=0. (a), (b) m=1, (c) m=2, and (d) m=3.

Fig. 4.
Fig. 4.

WF W(α,β) in phase space for several different parameter values m and θ with φ=π/4 and r=0.3. (a), (b) m=1, θ=0; (c) m=1, θ=π; and (d) m=2, θ=0.

Fig. 5.
Fig. 5.

Contour graph of WF W(α,β) in (Q+,P+) phase space for several different parameter values m, φ, and θ with r=0.3. Rows 1 and 2 correspond to φ=π/4, θ=π/6 and φ=θ=π/3, respectively. Columns 1, 2, and 3 correspond to m=1, 2, 3, respectively.

Fig. 6.
Fig. 6.

Graph of SVm as the function of φ and r. (a) m=2, (b) m=3, and (c) m=4.

Fig. 7.
Fig. 7.

EPR correlation Im as the function of φ and r. (a) m=1, (b) m=2, and (c) m=3.

Fig. 8.
Fig. 8.

Lower bound of entanglement of the CPA-TMSV, with (a)–(c) corresponding to m=1, 2, 3, respectively.

Fig. 9.
Fig. 9.

Fidelity of teleportation of coherent states using the CPA-TMSV as an entanglement resource, with (a)–(c) corresponding to m=0, 1, 2, respectively.

Equations (53)

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

|Ψ=Nm,φ(acosφ+eiθbsinφ)mS(r)|00,
S(r)|00=sechrexp(abtanhr)|00
|Ψ=Nm,φsechrmτmeabtanhr+τacosφ+τeiθbsinφ|00|τ=0.
Nm,φ2=m!χmcosh2mrPm(1/χ),
|r,k,lakblS|00=Ss=0min(k,l)k!l!tanhsrcoshk+lrs!(ks)!(ls)!|ks,ls;
r,k,l|r,k,l=δkk,llVk,l,k,l(r),
Vk,l,k,l(r)=s=0min(k,l)k!l!k!l!tanhkk+2srcosh2(k+l)rs!(ks)!(ls)!(kk+s)!.
Vl,k,l,k=Vk,l,k,l,
Vk,l,k,l=Vk,l,k,l.
|Ψ=n=0mei(mn)θAn|r,n,mn,
An=m!Nm,φn!(mn)!sinmnφcosnφ;
O^=n,n=0mei(nn)θAnAnr,n,mn|O^|r,n,mn,
aa=n=0mAn2Vn+1,mn,n+1,mn,
bb=n=0mAn2Vn,mn+1,n,mn+1,
aabb=n=0mAn2Vn+1,mn+1,n+1,mn+1.
gm,φ=0=1m+tanh2r,
g1=(cos4φ+2cosh4r3)cos4φ+8cosh2r4cosh4r5,
Raba2a2+b2b22aabb1<0.
a2a2=n=0mAn2Vn+2,mn,n+2,mn,b2b2=n=0mAn2Vn,mn+2,n,mn+2.
Rab,φ=0=m(m1)csch2r2(m+1)2(m+1)(mcosh2r+cosh2r),
Rab,m=1=23cosh2r+1.
Rab,m=2={53cosh2r6(1+2cosh2r)csch2r,φ=0,π2,π4(7+9cosh2r)sinh2r9cosh6r+3cosh4rcosh2r3,φ=π4,3π4,
Rab,m=3={52cosh2r2(3+5cosh2r)csch2r,φ=0,π2,π16(2+5cosh2r)sinh2r25cosh6r+11cosh2r6cosh4r6,φ=π4,3π4,
W(α,β)=e2(|α|2+|β|2)d2z1d2z2π4z1,z2|ρ|z1,z2×exp[2(αz1*α*z1)+2(βz2*β*z2)],
Wm,φ(α,β)=W0(α,β)Fm,φ(α,β),
W0(α,β)=1π2exp{2(|α|2+|β|2)cosh2r+2(αβ+α*β*)sinh2r},
Fm,φ(α,β)=l=0m(m!)2(cosh2r)lB2mlNm,φ2l![(ml)!]2|Hml[B1eiθ/2iB2]|2,
Wm,φ=0,π(α,β)=W0(α,β)(1)m×Lm(4|αcoshrβ*sinhr|2),
Wm,φ=π/2(α,β)=W0(α,β)(1)m×Lm(4|βcoshrα*sinhr|2).
Wm,φ(α,β)=(1)mπ2e2(|α|2+|β|2)×Lm(4|αcosφ+eiθβsinφ|2),
W1,φ(α,β)=W0(α,β)cosh2r(4|B1|2cosh2r),
SVmaa12bb12abab<0.
ab=n=0mAn2Vn,mn,n+1,mn+1,ab=n=0mAn2Vn+1,mn+1,n,mn.
SVm,φ=0=14[5+2m(4m+1)cosh2r],
ImΔQ2+ΔP+2<1.
Im=aa+bbabab1.
Σij=12X^iX^j+X^jX^iX^iX^j,
Σ=(uμμTυ),
μ=(QaQbQaPbQbPaPaPb),u=(Qa2QaPa+PaQa/2QaPa+PaQa/2Pa2),υ=(Qb2QbPb+PbQb/2QbPb+PbQb/2Pb2).
ΣC=(aa+1/2a2ababa2aa+1/2ababababbb+1/2b2ababb2bb+1/2),
Σ=MΣCM,
n˜±=Δ(Σ)±(Δ(Σ)24detΣ)1/22
EN=max[0,ln2n˜s].
a2=eiθn=0m1AnAn+1Vn+2,mn,n+1,mn1=a2*,b2=eiθn=0m1AnAn+1Vn+1,mn+1,n,mn=b2*,ab=eiθn=0m1AnAn+1Vn+1,mn,n+1,mn=ab*.
ΣC=12(cosh2r00sinh2r0cosh2rsinh2r00sinh2rcosh2r0sinh2r00cosh2r),
Σ=12(cosh2r0sinh2r00cosh2r0sinh2rsinh2r0cosh2r00sinh2r0cosh2r),
n˜s=Δ1Δ22f[cos22φ,cosh22r],
χ(α,β)=χ0(α,β)Cm,φ(α,β),
χ0(α,β)=e12(α*β*+αβ)sinh2r12(|α|2+|β|2)cosh2r,
Cm,φ(α,β)=Nm,φ2n=0m(m!)2(B2)mnB3nn![(mn)!]2|Hmn[B1eiθ/22iB2]|2.
F=d2ηπχin(η)χout(η).
Fm,φ=Nm,φ2σm+mτmsmeA(eiθs2+eiθτ2)+2Cτs|τ,s=0,
Fm,φ=2mm!σNm,φ2Dm/2Pm(C/D),

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