Abstract

We propose two experimental schemes that can produce an arbitrary photon-number entangled state (PNES) in a finite dimension. This class of entangled states naturally includes non-Gaussian continuous-variable (CV) states that may provide some practical advantages over the Gaussian counterparts (two-mode squeezed states). We particularly compare the entanglement characteristics of the Gaussian and the non-Gaussian states in view of the degree of entanglement and the Einstein-Podolsky-Rosen correlation, and further discuss their applications to the CV teleportation and the nonlocality test. The experimental imperfection due to the on-off photodetectors with nonideal efficiency is also considered in our analysis to show the feasibility of our schemes within existing technologies.

© 2012 OSA

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  27. M. Allegra, P. Giorda, and M. G. A. Paris, “Decoherence of Gaussian and nonGaussian photon-number entangled states in a noisy channel,” Int. J. Quant. Inf. 9, 27–38 (2011).
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  28. K. K. Sabapathy, J. S. Ivan, and R. Simon, “Robustness of non-Gaussian entanglement against noisy amplifier and attenuator environments,” Phys. Rev. Lett. 107, 130501 (2011).
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  29. J. Lee, M. S. Kim, and H. Nha, “Comment on “Role of initial entanglement and non-Gaussianity in the decoherence of photon-number entangled states evolving in a noisy channel”,” Phys. Rev. Lett. 107, 238901 (2011).
    [CrossRef] [PubMed]
  30. H. Nha, S.-Y. Lee, S.-W. Ji, and M. S. Kim, “Efficient entanglement criteria beyond Gaussian limits using Gaussian measurements,” Phys. Rev. Lett. 108, 030503 (2012).
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  31. H. Nha, G.-J. Milburn, and H. J. Carmichael, “Linear amplification and quantum cloning for non-Gaussian continuous variables,” New J. Phys. 12, 103010 (2010).
    [CrossRef]
  32. G. S. Agarwal, “Generation of pair coherent states and squeezing via the competition of four-wave mixing and amplified spontaneous emission,” Phys. Rev. Lett. 57, 827–830 (1986).
    [CrossRef] [PubMed]
  33. C. C. Gerry, J. Mimih, and R. Birrittella, “State-projective scheme for generating pair coherent states in traveling-wave optical fields,” Phys. Rev. A 84, 023810 (2011).
    [CrossRef]
  34. A. Gábris and G. S. Agarwal, “Quantuem teleportation with pair-coherent states,” Int. J. Quantum Inf. 5, 305–309 (2007).
    [CrossRef]
  35. C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).
    [CrossRef]
  36. A. Gilchrist, P. Deuar, and M. D. Reid, “Contradiction of quantum mechanics with local hidden variables for quadrature phase amplitude measurements,” Phys. Rev. Lett. 80, 3169–3172 (1998).
    [CrossRef]
  37. S. Daffer and P. L. Knight, “Generating optimal states for a homodyne Bell test,” Phys. Rev. A 72, 034101 (2005).
    [CrossRef]
  38. W. J. Munro, “Optimal states for Bell-inequality violations using quadrature-phase homodyne measurements,” Phys. Rev. A 59, 4197–4201 (1999).
    [CrossRef]
  39. J. Wenger, M. Hafezi, F. Grosshans, R. Tualle-Brouri, and P. Grangier, “Maximal violation of Bell inequalities using continuous-variable measurements,” Phys. Rev. A 67, 012105 (2003).
    [CrossRef]
  40. M. S. Kim, H. Jeong, A. Zavatta, V. Parigi, and M. Bellini, “Scheme for proving the bosonic commutation relation using single-photon interference,” Phys. Rev. Lett. 101, 260401 (2008).
    [CrossRef]
  41. 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] [PubMed]
  42. J. Park, S.-Y. Lee, H.-J. Kim, and H.-W. Lee, “Cavity-QED-based scheme for verification of the photon commutation relation,” New J. Phys. 12, 033019 (2010).
    [CrossRef]
  43. H.-J. Kim, J. Park, and H.-W. Lee, “Cavity-QED based scheme for realization of photon annihilation and creation operations and their combinations,” J. Opt. Soc. Am. B 27, 464–475 (2010).
    [CrossRef]
  44. A. Zavatta, J. Fiurasek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52 (2011)
    [CrossRef]
  45. 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]
  46. J. Park, S.-Y. Lee, H.-W. Lee, and H. Nha, “Enhanced Bell violation by a coherent superposition of photon subtraction and addition,” J. Opt. Soc. Am. B 29, 906–911 (2012).
    [CrossRef]
  47. K. Banaszek and K. Wódkiewicz, “Nonlocality of the Einstein–Podolsky–Rosen state in the Wigner representation,” Phys. Rev. A 58, 4345–4347 (1998).
    [CrossRef]
  48. K. Banaszek and K. Wódkiewicz, “Testing quantum nonlocality in phase space,” Phys. Rev. Lett. 82, 2009–2013 (1999).
    [CrossRef]
  49. A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
    [CrossRef] [PubMed]
  50. A recent experiment achieved a higher-squeezing level ∼6.8dB of a pulsed light at the wavelength λ =1500nm in optical fiber [51]. For a long-distance quantum communication, however, one may require a quantum memory to store the quantum state of light. For this purpose, alkali atoms have been employed with the wavelength range λ ∼800nm, e.g. [52]. Furthermore, the thermal photon noise that can be detrimental to the quantum nature of light usually increases with the wavelength, so we here compare the PNES with the pulsed squeezed light of λ =850nm reported in [49].
  51. R. Dong, J. Heersink, J. F. Corney, P. D. Drummond, U. L. Andersen, and G. Leuchs, “Experimental evidence for Raman-induced limits to efficient squeezing in optical fibers,” Opt. Lett. 33, 116–118 (2008).
    [CrossRef] [PubMed]
  52. B. Julsgarrd, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432, 482–486 (2004).
    [CrossRef]
  53. P. Marian and T. A. Marian, “Continuous-variable teleportation in the characteristic-function description,” Phys. Rev. A 74, 042306 (2006).
    [CrossRef]
  54. H. Jeong, W. Son, M. S. Kim, D. Ahn, and C. Brukner, “Quantum nonlocality test for continuous-variable states with dichotomic observables,” Phys. Rev. A 67, 012106 (2003).
    [CrossRef]
  55. S. M. Barnett and P. M. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 1997).
  56. D. T. Pegg, L. S. Phillips, and S. M. Barnett, “Optical state truncation by projection synthesis,” Phys. Rev. Lett. 81, 1604–1606 (1998).
    [CrossRef]
  57. G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).
    [CrossRef]
  58. D. Mogilevtsev, “Diagonal element inference by direct detection,” Opt. Commun. 156, 307–310 (1998).
    [CrossRef]
  59. D. Mogilevtsev, “Reconstruction of quantum states with binary detectors,” Acta Phys. Slov. 49, 743–478 (1999).
  60. A. R. Rossi, S. Olivares, and M. G. A. Paris, “Photon statistics without counting photons,” Phys. Rev. A 70, 055801 (2004).
    [CrossRef]
  61. D. Achilles, C. Silberhorn, C. Œliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. 28, 2387–2389 (2003).
    [CrossRef] [PubMed]
  62. M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68, 043814 (2003).
    [CrossRef]
  63. G. Brida, M. Genovese, M. Gramegna, M. G. A. Paris, E. Predazzi, and E. Cagliero, “On the reconstruction of diagonal elements of density matrix of quantum optical states by on/off detectors,” Open Syst. Inf. Dyn. 13, 333–341 (2006).
    [CrossRef]
  64. A. Tipsmark, R. Dong, A. Laghaout, P. Marek, M. Jezek, and U. L. Andersen, “Experimental demonstration of a Hadamard gate for coherent state qubits,” Phys. Rev. A 84, 050301(R) (2011).
    [CrossRef]

2012

2011

A. Zavatta, J. Fiurasek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52 (2011)
[CrossRef]

A. Tipsmark, R. Dong, A. Laghaout, P. Marek, M. Jezek, and U. L. Andersen, “Experimental demonstration of a Hadamard gate for coherent state qubits,” Phys. Rev. A 84, 050301(R) (2011).
[CrossRef]

C. C. Gerry, J. Mimih, and R. Birrittella, “State-projective scheme for generating pair coherent states in traveling-wave optical fields,” Phys. Rev. A 84, 023810 (2011).
[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]

M. Allegra, P. Giorda, and M. G. A. Paris, “Decoherence of Gaussian and nonGaussian photon-number entangled states in a noisy channel,” Int. J. Quant. Inf. 9, 27–38 (2011).
[CrossRef]

K. K. Sabapathy, J. S. Ivan, and R. Simon, “Robustness of non-Gaussian entanglement against noisy amplifier and attenuator environments,” Phys. Rev. Lett. 107, 130501 (2011).
[CrossRef] [PubMed]

J. Lee, M. S. Kim, and H. Nha, “Comment on “Role of initial entanglement and non-Gaussianity in the decoherence of photon-number entangled states evolving in a noisy channel”,” Phys. Rev. Lett. 107, 238901 (2011).
[CrossRef] [PubMed]

T. Kiesel, W. Vogel, and B. Hage, “Entangled qubits in a non-Gaussian quantum state,” Phys. Rev. A 83, 062319 (2011).
[CrossRef]

2010

F. Dell’Anno, S. De Siena, and F. Illuminati, “Realistic continuous-variable quantum teleportation with non-Gaussian resources,” Phys. Rev. A 81, 012333 (2010).
[CrossRef]

M. Allegra, P. Giorda, and M. G. A. Paris, “Role of initial entanglement and non-Gaussianity in the decoherence of photon-number entangled states evolving in a noisy channel,” Phys. Rev. Lett. 105, 100503 (2010).
[CrossRef] [PubMed]

H. Nha, G.-J. Milburn, and H. J. Carmichael, “Linear amplification and quantum cloning for non-Gaussian continuous variables,” New J. Phys. 12, 103010 (2010).
[CrossRef]

C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (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]

J. Park, S.-Y. Lee, H.-J. Kim, and H.-W. Lee, “Cavity-QED-based scheme for verification of the photon commutation relation,” New J. Phys. 12, 033019 (2010).
[CrossRef]

H.-J. Kim, J. Park, and H.-W. Lee, “Cavity-QED based scheme for realization of photon annihilation and creation operations and their combinations,” J. Opt. Soc. Am. B 27, 464–475 (2010).
[CrossRef]

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).
[CrossRef]

2009

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] [PubMed]

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

R. Dong, J. Heersink, J. F. Corney, P. D. Drummond, U. L. Andersen, and G. Leuchs, “Experimental evidence for Raman-induced limits to efficient squeezing in optical fibers,” Opt. Lett. 33, 116–118 (2008).
[CrossRef] [PubMed]

M. S. Kim, H. Jeong, A. Zavatta, V. Parigi, and M. Bellini, “Scheme for proving the bosonic commutation relation using single-photon interference,” Phys. Rev. Lett. 101, 260401 (2008).
[CrossRef]

2007

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

F. Dell’Anno, S. De Siena, L. Albano, and F. Illuminati, “Continuous-variable quantum teleportation with non-Gaussian resources,” Phys. Rev. A 76, 022301 (2007).
[CrossRef]

A. Gábris and G. S. Agarwal, “Quantuem teleportation with pair-coherent states,” Int. J. Quantum Inf. 5, 305–309 (2007).
[CrossRef]

2006

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]

G. Brida, M. Genovese, M. Gramegna, M. G. A. Paris, E. Predazzi, and E. Cagliero, “On the reconstruction of diagonal elements of density matrix of quantum optical states by on/off detectors,” Open Syst. Inf. Dyn. 13, 333–341 (2006).
[CrossRef]

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

2005

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[CrossRef]

M. Genovese, “Research on hidden variable theories: a review of recent progresses,” Phys. Rep. 413, 319–396. (2005).
[CrossRef]

S. Daffer and P. L. Knight, “Generating optimal states for a homodyne Bell test,” Phys. Rev. A 72, 034101 (2005).
[CrossRef]

A. Kitagawa, M. Takeoka, K. Wakui, and M. Sasaki, “Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to the dense coding scheme,” Phys. Rev. A 72, 022334 (2005).
[CrossRef]

2004

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

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] [PubMed]

B. Julsgarrd, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432, 482–486 (2004).
[CrossRef]

A. R. Rossi, S. Olivares, and M. G. A. Paris, “Photon statistics without counting photons,” Phys. Rev. A 70, 055801 (2004).
[CrossRef]

2003

D. Achilles, C. Silberhorn, C. Œliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. 28, 2387–2389 (2003).
[CrossRef] [PubMed]

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68, 043814 (2003).
[CrossRef]

H. Jeong, W. Son, M. S. Kim, D. Ahn, and C. Brukner, “Quantum nonlocality test for continuous-variable states with dichotomic observables,” Phys. Rev. A 67, 012106 (2003).
[CrossRef]

J. Wenger, M. Hafezi, F. Grosshans, R. Tualle-Brouri, and P. Grangier, “Maximal violation of Bell inequalities using continuous-variable measurements,” Phys. Rev. A 67, 012105 (2003).
[CrossRef]

S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleportation improvement by inconclusive photon subtraction,” Phys. Rev. A 67, 032314 (2003).
[CrossRef]

2002

P. T. Cochrane, T. C. Ralph, and G. J. Milburn, “Teleportation improvement by conditional measurements on the two-mode squeezed vacuum,” Phys. Rev. A 65, 062306 (2002).
[CrossRef]

S. D. Bartlett and B. C. Sanders, “Efficient classical simulation of optical quantum information circuits,” Phys. Rev. Lett. 89, 207903 (2002).
[CrossRef] [PubMed]

2000

T. Opatrný, G. Kurizki, and D.-G. Welsch, “Improvement on teleportation of continuous variables by photon subtraction via conditional measurement,” Phys. Rev. A 61, 032302 (2000).
[CrossRef]

1999

S. Lloyd and S. L. Braunstein, “Quantum computation over continuous variables,” Phys. Rev. Lett. 82, 1784– 1787 (1999).
[CrossRef]

W. J. Munro, “Optimal states for Bell-inequality violations using quadrature-phase homodyne measurements,” Phys. Rev. A 59, 4197–4201 (1999).
[CrossRef]

K. Banaszek and K. Wódkiewicz, “Testing quantum nonlocality in phase space,” Phys. Rev. Lett. 82, 2009–2013 (1999).
[CrossRef]

D. Mogilevtsev, “Reconstruction of quantum states with binary detectors,” Acta Phys. Slov. 49, 743–478 (1999).

1998

D. T. Pegg, L. S. Phillips, and S. M. Barnett, “Optical state truncation by projection synthesis,” Phys. Rev. Lett. 81, 1604–1606 (1998).
[CrossRef]

D. Mogilevtsev, “Diagonal element inference by direct detection,” Opt. Commun. 156, 307–310 (1998).
[CrossRef]

K. Banaszek and K. Wódkiewicz, “Nonlocality of the Einstein–Podolsky–Rosen state in the Wigner representation,” Phys. Rev. A 58, 4345–4347 (1998).
[CrossRef]

A. Gilchrist, P. Deuar, and M. D. Reid, “Contradiction of quantum mechanics with local hidden variables for quadrature phase amplitude measurements,” Phys. Rev. Lett. 80, 3169–3172 (1998).
[CrossRef]

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

1993

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

1986

G. S. Agarwal, “Generation of pair coherent states and squeezing via the competition of four-wave mixing and amplified spontaneous emission,” Phys. Rev. Lett. 57, 827–830 (1986).
[CrossRef] [PubMed]

1969

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[CrossRef]

1964

J. S. Bell, “On the Einstein–Podolsky–Rosen paradox,” Physics 1, 195–200 (1964).

1935

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. Lett. 47, 777–780 (1935).

Achilles, D.

Agarwal, G. S.

A. Gábris and G. S. Agarwal, “Quantuem teleportation with pair-coherent states,” Int. J. Quantum Inf. 5, 305–309 (2007).
[CrossRef]

G. S. Agarwal, “Generation of pair coherent states and squeezing via the competition of four-wave mixing and amplified spontaneous emission,” Phys. Rev. Lett. 57, 827–830 (1986).
[CrossRef] [PubMed]

Ahn, D.

H. Jeong, W. Son, M. S. Kim, D. Ahn, and C. Brukner, “Quantum nonlocality test for continuous-variable states with dichotomic observables,” Phys. Rev. A 67, 012106 (2003).
[CrossRef]

Albano, L.

F. Dell’Anno, S. De Siena, L. Albano, and F. Illuminati, “Continuous-variable quantum teleportation with non-Gaussian resources,” Phys. Rev. A 76, 022301 (2007).
[CrossRef]

Allegra, M.

M. Allegra, P. Giorda, and M. G. A. Paris, “Decoherence of Gaussian and nonGaussian photon-number entangled states in a noisy channel,” Int. J. Quant. Inf. 9, 27–38 (2011).
[CrossRef]

M. Allegra, P. Giorda, and M. G. A. Paris, “Role of initial entanglement and non-Gaussianity in the decoherence of photon-number entangled states evolving in a noisy channel,” Phys. Rev. Lett. 105, 100503 (2010).
[CrossRef] [PubMed]

Andersen, U. L.

A. Tipsmark, R. Dong, A. Laghaout, P. Marek, M. Jezek, and U. L. Andersen, “Experimental demonstration of a Hadamard gate for coherent state qubits,” Phys. Rev. A 84, 050301(R) (2011).
[CrossRef]

R. Dong, J. Heersink, J. F. Corney, P. D. Drummond, U. L. Andersen, and G. Leuchs, “Experimental evidence for Raman-induced limits to efficient squeezing in optical fibers,” Opt. Lett. 33, 116–118 (2008).
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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).
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H. Nha, S.-Y. Lee, S.-W. Ji, and M. S. Kim, “Efficient entanglement criteria beyond Gaussian limits using Gaussian measurements,” Phys. Rev. Lett. 108, 030503 (2012).
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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. Nha, G.-J. Milburn, and H. J. Carmichael, “Linear amplification and quantum cloning for non-Gaussian continuous variables,” New J. Phys. 12, 103010 (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]

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

Nogueira, W. A. T.

Œliwa, C.

Olivares, S.

A. R. Rossi, S. Olivares, and M. G. A. Paris, “Photon statistics without counting photons,” Phys. Rev. A 70, 055801 (2004).
[CrossRef]

S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleportation improvement by inconclusive photon subtraction,” Phys. Rev. A 67, 032314 (2003).
[CrossRef]

Opatrný, T.

T. Opatrný, G. Kurizki, and D.-G. Welsch, “Improvement on teleportation of continuous variables by photon subtraction via conditional measurement,” Phys. Rev. A 61, 032302 (2000).
[CrossRef]

Ourjoumtsev, A.

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

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] [PubMed]

M. S. Kim, H. Jeong, A. Zavatta, V. Parigi, and M. Bellini, “Scheme for proving the bosonic commutation relation using single-photon interference,” Phys. Rev. Lett. 101, 260401 (2008).
[CrossRef]

Paris, M. G. A.

M. Allegra, P. Giorda, and M. G. A. Paris, “Decoherence of Gaussian and nonGaussian photon-number entangled states in a noisy channel,” Int. J. Quant. Inf. 9, 27–38 (2011).
[CrossRef]

M. Allegra, P. Giorda, and M. G. A. Paris, “Role of initial entanglement and non-Gaussianity in the decoherence of photon-number entangled states evolving in a noisy channel,” Phys. Rev. Lett. 105, 100503 (2010).
[CrossRef] [PubMed]

G. Brida, M. Genovese, M. Gramegna, M. G. A. Paris, E. Predazzi, and E. Cagliero, “On the reconstruction of diagonal elements of density matrix of quantum optical states by on/off detectors,” Open Syst. Inf. Dyn. 13, 333–341 (2006).
[CrossRef]

A. R. Rossi, S. Olivares, and M. G. A. Paris, “Photon statistics without counting photons,” Phys. Rev. A 70, 055801 (2004).
[CrossRef]

S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleportation improvement by inconclusive photon subtraction,” Phys. Rev. A 67, 032314 (2003).
[CrossRef]

Park, J.

Pegg, D. T.

D. T. Pegg, L. S. Phillips, and S. M. Barnett, “Optical state truncation by projection synthesis,” Phys. Rev. Lett. 81, 1604–1606 (1998).
[CrossRef]

Peres, A.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

Phillips, L. S.

D. T. Pegg, L. S. Phillips, and S. M. Barnett, “Optical state truncation by projection synthesis,” Phys. Rev. Lett. 81, 1604–1606 (1998).
[CrossRef]

Pirandola, S.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” arXiv:1110.3234 [quant-ph] (2011).

Pittman, T. B.

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68, 043814 (2003).
[CrossRef]

Podolsky, B.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. Lett. 47, 777–780 (1935).

Polzik, E. S.

B. Julsgarrd, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432, 482–486 (2004).
[CrossRef]

Predazzi, E.

G. Brida, M. Genovese, M. Gramegna, M. G. A. Paris, E. Predazzi, and E. Cagliero, “On the reconstruction of diagonal elements of density matrix of quantum optical states by on/off detectors,” Open Syst. Inf. Dyn. 13, 333–341 (2006).
[CrossRef]

Pryde, G. J.

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).
[CrossRef]

Radmore, P. M.

S. M. Barnett and P. M. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 1997).

Ralph, T. C.

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).
[CrossRef]

P. T. Cochrane, T. C. Ralph, and G. J. Milburn, “Teleportation improvement by conditional measurements on the two-mode squeezed vacuum,” Phys. Rev. A 65, 062306 (2002).
[CrossRef]

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” arXiv:1110.3234 [quant-ph] (2011).

Reid, M. D.

A. Gilchrist, P. Deuar, and M. D. Reid, “Contradiction of quantum mechanics with local hidden variables for quadrature phase amplitude measurements,” Phys. Rev. Lett. 80, 3169–3172 (1998).
[CrossRef]

Rosen, N.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. Lett. 47, 777–780 (1935).

Rossi, A. R.

A. R. Rossi, S. Olivares, and M. G. A. Paris, “Photon statistics without counting photons,” Phys. Rev. A 70, 055801 (2004).
[CrossRef]

Sabapathy, K. K.

K. K. Sabapathy, J. S. Ivan, and R. Simon, “Robustness of non-Gaussian entanglement against noisy amplifier and attenuator environments,” Phys. Rev. Lett. 107, 130501 (2011).
[CrossRef] [PubMed]

Sanders, B. C.

S. D. Bartlett and B. C. Sanders, “Efficient classical simulation of optical quantum information circuits,” Phys. Rev. Lett. 89, 207903 (2002).
[CrossRef] [PubMed]

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]

A. Kitagawa, M. Takeoka, K. Wakui, and M. Sasaki, “Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to the dense coding scheme,” Phys. Rev. A 72, 022334 (2005).
[CrossRef]

Shapiro, J. H.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” arXiv:1110.3234 [quant-ph] (2011).

Sherson, J.

B. Julsgarrd, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432, 482–486 (2004).
[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, 880–884 (1969).
[CrossRef]

Shor, P. W.

P. W. Shor, “Algorithms for quantum computer computation: discrete logarithms and factoring,” in Proceedings of the Symposium on the Foundations of Computer Science, Los Alamitos, California (IEEE, 1994), pp. 124–134.

Silberhorn, C.

Simon, R.

K. K. Sabapathy, J. S. Ivan, and R. Simon, “Robustness of non-Gaussian entanglement against noisy amplifier and attenuator environments,” Phys. Rev. Lett. 107, 130501 (2011).
[CrossRef] [PubMed]

Son, W.

H. Jeong, W. Son, M. S. Kim, D. Ahn, and C. Brukner, “Quantum nonlocality test for continuous-variable states with dichotomic observables,” Phys. Rev. A 67, 012106 (2003).
[CrossRef]

Takeda, S.

S. Takeda, H. Benichi, T. Mizuta, N. Lee, J. Yoshikawa, and A. Furusawa, “Quantum mode filtering of non-Gaussian states for teleportation-based quantum information processing,” arXiv:1202.2418.

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]

A. Kitagawa, M. Takeoka, K. Wakui, and M. Sasaki, “Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to the dense coding scheme,” Phys. Rev. A 72, 022334 (2005).
[CrossRef]

Tipsmark, A.

A. Tipsmark, R. Dong, A. Laghaout, P. Marek, M. Jezek, and U. L. Andersen, “Experimental demonstration of a Hadamard gate for coherent state qubits,” Phys. Rev. A 84, 050301(R) (2011).
[CrossRef]

Tualle-Brouri, R.

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

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] [PubMed]

J. Wenger, M. Hafezi, F. Grosshans, R. Tualle-Brouri, and P. Grangier, “Maximal violation of Bell inequalities using continuous-variable measurements,” Phys. Rev. A 67, 012105 (2003).
[CrossRef]

van Loock, P.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[CrossRef]

Vogel, W.

T. Kiesel, W. Vogel, and B. Hage, “Entangled qubits in a non-Gaussian quantum state,” Phys. Rev. A 83, 062319 (2011).
[CrossRef]

Wakui, K.

A. Kitagawa, M. Takeoka, K. Wakui, and M. Sasaki, “Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to the dense coding scheme,” Phys. Rev. A 72, 022334 (2005).
[CrossRef]

Walk, N.

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).
[CrossRef]

Walmsley, I. A.

Weedbrook, C.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” arXiv:1110.3234 [quant-ph] (2011).

Welsch, D.-G.

T. Opatrný, G. Kurizki, and D.-G. Welsch, “Improvement on teleportation of continuous variables by photon subtraction via conditional measurement,” Phys. Rev. A 61, 032302 (2000).
[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] [PubMed]

J. Wenger, M. Hafezi, F. Grosshans, R. Tualle-Brouri, and P. Grangier, “Maximal violation of Bell inequalities using continuous-variable measurements,” Phys. Rev. A 67, 012105 (2003).
[CrossRef]

Wódkiewicz, K.

K. Banaszek and K. Wódkiewicz, “Testing quantum nonlocality in phase space,” Phys. Rev. Lett. 82, 2009–2013 (1999).
[CrossRef]

K. Banaszek and K. Wódkiewicz, “Nonlocality of the Einstein–Podolsky–Rosen state in the Wigner representation,” Phys. Rev. A 58, 4345–4347 (1998).
[CrossRef]

Wootters, W. K.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

Xiang, G. Y.

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).
[CrossRef]

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]

Yoshikawa, J.

S. Takeda, H. Benichi, T. Mizuta, N. Lee, J. Yoshikawa, and A. Furusawa, “Quantum mode filtering of non-Gaussian states for teleportation-based quantum information processing,” arXiv:1202.2418.

Zavatta, A.

A. Zavatta, J. Fiurasek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52 (2011)
[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] [PubMed]

M. S. Kim, H. Jeong, A. Zavatta, V. Parigi, and M. Bellini, “Scheme for proving the bosonic commutation relation using single-photon interference,” Phys. Rev. Lett. 101, 260401 (2008).
[CrossRef]

Acta Phys. Slov.

D. Mogilevtsev, “Reconstruction of quantum states with binary detectors,” Acta Phys. Slov. 49, 743–478 (1999).

Int. J. Quant. Inf.

M. Allegra, P. Giorda, and M. G. A. Paris, “Decoherence of Gaussian and nonGaussian photon-number entangled states in a noisy channel,” Int. J. Quant. Inf. 9, 27–38 (2011).
[CrossRef]

Int. J. Quantum Inf.

A. Gábris and G. S. Agarwal, “Quantuem teleportation with pair-coherent states,” Int. J. Quantum Inf. 5, 305–309 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photonics

A. Zavatta, J. Fiurasek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52 (2011)
[CrossRef]

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).
[CrossRef]

Nature

B. Julsgarrd, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432, 482–486 (2004).
[CrossRef]

New J. Phys.

J. Park, S.-Y. Lee, H.-J. Kim, and H.-W. Lee, “Cavity-QED-based scheme for verification of the photon commutation relation,” New J. Phys. 12, 033019 (2010).
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H. Nha, G.-J. Milburn, and H. J. Carmichael, “Linear amplification and quantum cloning for non-Gaussian continuous variables,” New J. Phys. 12, 103010 (2010).
[CrossRef]

Open Syst. Inf. Dyn.

G. Brida, M. Genovese, M. Gramegna, M. G. A. Paris, E. Predazzi, and E. Cagliero, “On the reconstruction of diagonal elements of density matrix of quantum optical states by on/off detectors,” Open Syst. Inf. Dyn. 13, 333–341 (2006).
[CrossRef]

Opt. Commun.

D. Mogilevtsev, “Diagonal element inference by direct detection,” Opt. Commun. 156, 307–310 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rep.

M. Genovese, “Research on hidden variable theories: a review of recent progresses,” Phys. Rep. 413, 319–396. (2005).
[CrossRef]

Phys. Rev. A

T. Opatrný, G. Kurizki, and D.-G. Welsch, “Improvement on teleportation of continuous variables by photon subtraction via conditional measurement,” Phys. Rev. A 61, 032302 (2000).
[CrossRef]

P. T. Cochrane, T. C. Ralph, and G. J. Milburn, “Teleportation improvement by conditional measurements on the two-mode squeezed vacuum,” Phys. Rev. A 65, 062306 (2002).
[CrossRef]

S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleportation improvement by inconclusive photon subtraction,” Phys. Rev. A 67, 032314 (2003).
[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]

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]

F. Dell’Anno, S. De Siena, L. Albano, and F. Illuminati, “Continuous-variable quantum teleportation with non-Gaussian resources,” Phys. Rev. A 76, 022301 (2007).
[CrossRef]

F. Dell’Anno, S. De Siena, and F. Illuminati, “Realistic continuous-variable quantum teleportation with non-Gaussian resources,” Phys. Rev. A 81, 012333 (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]

A. Kitagawa, M. Takeoka, K. Wakui, and M. Sasaki, “Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to the dense coding scheme,” Phys. Rev. A 72, 022334 (2005).
[CrossRef]

T. Kiesel, W. Vogel, and B. Hage, “Entangled qubits in a non-Gaussian quantum state,” Phys. Rev. A 83, 062319 (2011).
[CrossRef]

C. C. Gerry, J. Mimih, and R. Birrittella, “State-projective scheme for generating pair coherent states in traveling-wave optical fields,” Phys. Rev. A 84, 023810 (2011).
[CrossRef]

C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).
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S. Daffer and P. L. Knight, “Generating optimal states for a homodyne Bell test,” Phys. Rev. A 72, 034101 (2005).
[CrossRef]

W. J. Munro, “Optimal states for Bell-inequality violations using quadrature-phase homodyne measurements,” Phys. Rev. A 59, 4197–4201 (1999).
[CrossRef]

J. Wenger, M. Hafezi, F. Grosshans, R. Tualle-Brouri, and P. Grangier, “Maximal violation of Bell inequalities using continuous-variable measurements,” Phys. Rev. A 67, 012105 (2003).
[CrossRef]

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68, 043814 (2003).
[CrossRef]

A. Tipsmark, R. Dong, A. Laghaout, P. Marek, M. Jezek, and U. L. Andersen, “Experimental demonstration of a Hadamard gate for coherent state qubits,” Phys. Rev. A 84, 050301(R) (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]

A. R. Rossi, S. Olivares, and M. G. A. Paris, “Photon statistics without counting photons,” Phys. Rev. A 70, 055801 (2004).
[CrossRef]

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

H. Jeong, W. Son, M. S. Kim, D. Ahn, and C. Brukner, “Quantum nonlocality test for continuous-variable states with dichotomic observables,” Phys. Rev. A 67, 012106 (2003).
[CrossRef]

K. Banaszek and K. Wódkiewicz, “Nonlocality of the Einstein–Podolsky–Rosen state in the Wigner representation,” Phys. Rev. A 58, 4345–4347 (1998).
[CrossRef]

Phys. Rev. Lett.

K. Banaszek and K. Wódkiewicz, “Testing quantum nonlocality in phase space,” Phys. Rev. Lett. 82, 2009–2013 (1999).
[CrossRef]

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

D. T. Pegg, L. S. Phillips, and S. M. Barnett, “Optical state truncation by projection synthesis,” Phys. Rev. Lett. 81, 1604–1606 (1998).
[CrossRef]

M. S. Kim, H. Jeong, A. Zavatta, V. Parigi, and M. Bellini, “Scheme for proving the bosonic commutation relation using single-photon interference,” Phys. Rev. Lett. 101, 260401 (2008).
[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] [PubMed]

A. Gilchrist, P. Deuar, and M. D. Reid, “Contradiction of quantum mechanics with local hidden variables for quadrature phase amplitude measurements,” Phys. Rev. Lett. 80, 3169–3172 (1998).
[CrossRef]

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[CrossRef]

G. S. Agarwal, “Generation of pair coherent states and squeezing via the competition of four-wave mixing and amplified spontaneous emission,” Phys. Rev. Lett. 57, 827–830 (1986).
[CrossRef] [PubMed]

K. K. Sabapathy, J. S. Ivan, and R. Simon, “Robustness of non-Gaussian entanglement against noisy amplifier and attenuator environments,” Phys. Rev. Lett. 107, 130501 (2011).
[CrossRef] [PubMed]

J. Lee, M. S. Kim, and H. Nha, “Comment on “Role of initial entanglement and non-Gaussianity in the decoherence of photon-number entangled states evolving in a noisy channel”,” Phys. Rev. Lett. 107, 238901 (2011).
[CrossRef] [PubMed]

H. Nha, S.-Y. Lee, S.-W. Ji, and M. S. Kim, “Efficient entanglement criteria beyond Gaussian limits using Gaussian measurements,” Phys. Rev. Lett. 108, 030503 (2012).
[CrossRef] [PubMed]

S. Lloyd and S. L. Braunstein, “Quantum computation over continuous variables,” Phys. Rev. Lett. 82, 1784– 1787 (1999).
[CrossRef]

S. D. Bartlett and B. C. Sanders, “Efficient classical simulation of optical quantum information circuits,” Phys. Rev. Lett. 89, 207903 (2002).
[CrossRef] [PubMed]

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

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] [PubMed]

M. Allegra, P. Giorda, and M. G. A. Paris, “Role of initial entanglement and non-Gaussianity in the decoherence of photon-number entangled states evolving in a noisy channel,” Phys. Rev. Lett. 105, 100503 (2010).
[CrossRef] [PubMed]

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. Lett. 47, 777–780 (1935).

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

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

Physics

J. S. Bell, “On the Einstein–Podolsky–Rosen paradox,” Physics 1, 195–200 (1964).

Rev. Mod. Phys.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[CrossRef]

Other

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” arXiv:1110.3234 [quant-ph] (2011).

S. Takeda, H. Benichi, T. Mizuta, N. Lee, J. Yoshikawa, and A. Furusawa, “Quantum mode filtering of non-Gaussian states for teleportation-based quantum information processing,” arXiv:1202.2418.

P. W. Shor, “Algorithms for quantum computer computation: discrete logarithms and factoring,” in Proceedings of the Symposium on the Foundations of Computer Science, Los Alamitos, California (IEEE, 1994), pp. 124–134.

A recent experiment achieved a higher-squeezing level ∼6.8dB of a pulsed light at the wavelength λ =1500nm in optical fiber [51]. For a long-distance quantum communication, however, one may require a quantum memory to store the quantum state of light. For this purpose, alkali atoms have been employed with the wavelength range λ ∼800nm, e.g. [52]. Furthermore, the thermal photon noise that can be detrimental to the quantum nature of light usually increases with the wavelength, so we here compare the PNES with the pulsed squeezed light of λ =850nm reported in [49].

S. M. Barnett and P. M. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 1997).

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Figures (7)

Fig. 1
Fig. 1

(a) Degree of entanglement and (b) EPR correlation for the states: |TMSS〉 (blue solid) as a function of the squeezing parameter s, and n = 0 N C n | n a | n b at N = 1 (red dotted), N = 2 (red dashed), N = 10 (red dot-dashed).

Fig. 2
Fig. 2

(a) Average fidelity in teleporting a coherent state and (b) Bell parameter BBW as a function of the squeezing parameter s for the |TMSS〉 (blue solid) and the PNES n = 0 N C n | n a | n b at N = 1 (red dotted), N = 2 (red dashed) and N = 3 (red dot-dashed). The coefficients of the PNESs are optimized for each N.

Fig. 3
Fig. 3

(a) Experimental scheme to implement the operation S ^ a b ( ξ ) ( t a ^ a ^ + r a ^ a ^ ) S ^ a b ( ξ ) on an arbitrary state. BS1, BS2, and BS3 are beam splitters with transmissivities T1, T2 and tn, respectively. PD0, PD1 and PD2: photo detectors. The operation is successfully achieved under the detection of a single photon at only one of two detectors PD1 and PD2, with PD0 clicked. (b) For a vacuum input state, the sequence of operations Ôn can yield a finite dimensional PNES, n = 0 N C n | n a | n b.

Fig. 4
Fig. 4

Experimental scheme to implement the operation (t2nâ + r2nb̂)(t2n−1b̂ + r2n−1â) on an input state |ψab. BS1, BS2, BS3 and BS4 are beam splitters with transmissivities T1, T2, t2n−1, and t2n, respectively. PD1, PD2, PD3 and PD4: photo detectors. The operation is successfully achieved under the detection of a single photon at only one of two detectors PD1 and PD2 and the detection of a single-photon at only one of two detectors PD3 and PD4.

Fig. 5
Fig. 5

Fidelity between the ideal state C0|0〉a|0〉b + C1|1〉a|1〉b and the output state ρout obtained by applying S ^ a b ( ξ ) ( t a ^ a ^ + r a ^ a ^ ) S ^ a b ( ξ ) (blue circle) or (t2â + r2b̂)(t1b̂ + r1â) (red square), using on-off detectors with efficiency η to the input state ρin = |0〉a|0〉b as a function of |C0|2 for η = 0.66. Black triangle represents the output fidelity using the scissor scheme of [57], with the input two-mode squeezed state (s = 0.1) and the on-off detectors (η = 0.66).

Fig. 6
Fig. 6

Fidelity between the ideal state C0|0〉a|0〉b +C1|1〉a|1〉b +C2|2〉a|2〉b and the output state ρout obtained by applying twice (a) S ^ a b ( ξ 2 ) ( t 2 a ^ a ^ + r 2 a ^ a ^ ) S ^ a b ( ξ 2 ) S ^ a b ( ξ 1 ) ( t 1 a ^ a ^ + r 1 a ^ a ^ ) S ^ a b ( ξ 1 ) or (b) (t4â+r4b̂)(t3b̂+r3â)(t2â+r2b̂)(t1b̂+r1â), using on-off detectors with efficiency η to the input state ρin = |0〉a|0〉b as a function of |C1|2 and |C2|2 for η = 0.66.

Fig. 7
Fig. 7

Fidelity between the ideal state C0|0〉a|0〉b + C1|1〉a|1〉b and the output state with the error Δti = ±0.01 of the beam-splitter transmissivity (i = 1,2). Other parameters are the same as those in Fig. 6.

Equations (14)

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F = 1 π d 2 λ C out ( λ ) C in ( λ ) ,
C E ( λ 2 , λ 3 ) = e ( | λ 2 | 2 + | λ 3 | 2 ) / 2 [ | C 0 | 2 + | C 1 | 2 ( 1 | λ 2 | 2 ) ( 1 | λ 3 | 2 ) + | C 2 | 2 4 ( 2 4 | λ 2 | 2 + | λ 2 | 4 ) ( 2 4 | λ 3 | 2 + | λ 3 | 4 ) + C 0 * C 1 λ 2 * λ 3 * + C 0 C 1 * λ 2 λ 3 + C 0 * C 2 2 λ 2 * 2 λ 3 * 2 + C 0 C 2 * 2 λ 2 2 λ 3 2 + 1 2 ( C 1 * C 2 λ 2 * λ 3 * + C 1 C 2 * λ 2 λ 3 ) ( | λ 2 | 2 2 ) ( | λ 3 | 2 2 ) ] ,
B BW = π 2 4 | W ( α , β ) + W ( α , β ) + W ( α , β ) W ( α , β ) | 2 ,
O ^ n S ^ a b ( ξ n ) ( t n a ^ a ^ + r n a ^ a ^ ) S ^ a b ( ξ n ) = A n + ( t n + r n ) ( a ^ a ^ cosh 2 s n + b ^ b ^ sinh 2 s n ) ( t n + r n ) cosh s n sinh s n [ exp ( i φ n ) a ^ b ^ + exp ( i φ n ) a ^ b ^ ] ,
A n = t n cosh 2 s n + r n sinh 2 s n ,
B ^ a c S ^ a b ( ξ n ) | ψ a b | 0 c ( 1 R 1 * T 1 a ^ c ^ ) S ^ a b ( ξ n ) | ψ a b | 0 c .
1 | e S ^ a e ( 1 R 1 * T 1 a ^ c ^ ) S ^ a b ( ξ n ) | ψ a b | 0 c | 0 e s a ^ ( 1 R 1 * T 1 a ^ c ^ ) S ^ a b ( ξ n ) | ψ a b | 0 c ,
( s ) B ^ a d a ^ ( 1 R 1 * T 1 a ^ c ^ ) S ^ a b ( ξ n ) | ψ a b | 0 c d ( s ) ( 1 R 2 * T 2 a ^ d ^ ) a ^ ( 1 R 1 * T 1 a ^ c ^ ) S ^ a b ( ξ n ) | ψ a b | 0 c d ,
| S | ψ ( s ) [ 1 R 2 * T 2 a ^ ( t n d ^ r n c ^ ) ] a ^ [ 1 R 1 * T 1 a ^ ( t n c ^ + r n d ^ ) ] S ^ a b ( ξ n ) | ψ a b | 0 c d .
O ^ n ( t 2 n a ^ + r 2 n b ^ ) ( t 2 n 1 b ^ + r 2 n 1 a ^ ) = t 2 n 1 t 2 n a ^ b ^ + r 2 n 1 r 2 n a ^ b ^ + r 2 n 1 t 2 n a ^ a ^ + t 2 n 1 r 2 n b ^ b ^ ,
[ 1 R 1 * T 1 b ^ ( t 2 n 1 d ^ r 2 n 1 c ^ ) ] [ 1 s 1 a ^ ( t 2 n 1 c ^ + r 2 n 1 d ^ ) ] | ψ a b | 0 c d .
| S | ψ [ 1 R 2 * T 2 a ^ ( t 2 n e ^ + r 2 n f ^ ) ] [ 1 s 2 b ^ ( t 2 n f ^ + r 2 n e ^ ) ] | Φ a b | 0 e f .
ρ out = Tr c d e [ Π ^ 0 c Π ^ 1 d Π ^ 1 e U ^ 1 ρ in U ^ 1 ] Tr a b c d e [ Π ^ 0 c Π ^ 1 d Π ^ 1 e U ^ 1 ρ in U ^ 1 ] ,
ρ out = Tr c d e f [ Π ^ 0 e Π ^ 1 f Π ^ 0 c Π ^ 1 d U ^ 2 ρ in U ^ 2 ] Tr a b c d e f [ Π ^ 0 e Π ^ 1 f Π ^ 0 c Π ^ 1 d U ^ 2 ρ in U ^ 2 ] ,

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