Abstract

We investigate the nonclassical properties of multiple-photon-added displaced squeezed thermal states (PADSTSs). Particularly, we study the dependence of those nonclassical properties on the compound phase ϕθ/2 involved in squeezing and displacement parameters. We find that the Mandel Q parameter, the quadrature squeezing, the negative volume of the Wigner function, and the fidelity between PADSTSs and displaced squeezed thermal states (DSTSs) are all periodic functions of ϕθ/2 with a period π. Without considering the displacement parameter, these quantities are all phase independent. Finally, we investigate the non-Gaussianity of PADSTSs according to the fidelity between PADSTSs and DSTSs and find that non-Gaussianity and nonclassicality have similar behavior. Thus, the non-Gaussianity induced by the photon-addition operation is essentially nonclassical.

© 2012 Optical Society of America

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  43. J. Lee, J. Kim, and H. Nha, “Demonstrating higher-order nonclassical effects by photon-added classical states: realistic schemes,” J. Opt. Soc. Am. B 26, 1363–1369 (2009).
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2012 (2)

2011 (1)

2010 (7)

M. Barbieri, N. Spagnolo, M. G. Genoni, F. Ferreyrol, R. Blandino, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Non-Gaussianity of quantum states: an experimental test on single-photon-added coherent states,” Phys. Rev. A 82, 063833 (2010).
[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]

M. G. Genoni and M. G. A. Paris, “Quantifying non-Gaussianity for quantum information,” Phys. Rev. A 82, 052341(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]

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nat. Phys. 7, 13–16 (2010).
[CrossRef]

L. Y. Hu, X. X. Xu, Z. S. Wang, and X. F. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010).
[CrossRef]

X. X. Xu, L. Y. Hu, and H. Y. Fan, “Photon-added squeezed thermal states: Statistical properties and its decoherence in a photon-loss channel,” Opt. Commun. 283, 1801–1809 (2010).
[CrossRef]

2009 (4)

J. Calsamiglia, M. Aspachs, R. Munoz-Tapia, and E. Bagan, “Phase-covariant quantum benchmarks,” Phys. Rev. A 79, 050301 (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]

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]

J. Lee, J. Kim, and H. Nha, “Demonstrating higher-order nonclassical effects by photon-added classical states: realistic schemes,” J. Opt. Soc. Am. B 26, 1363–1369 (2009).
[CrossRef]

2008 (5)

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]

H. Y. Fan, “Newton–Leibniz integration for ket–bra operators in quantum mechanics (IV)—integrations within Weyl ordered product of operators and their applications,” Ann. Phys. 323, 500–526 (2008).
[CrossRef]

M. G. Genoni, M. G. A. Paris, and K. Banaszek, “Quantifying the non-Gaussian character of a quantum state by quantum relative entropy,” Phys. Rev. A 78, 060303 (2008).
[CrossRef]

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

M. Owari, M. B. Plenio, E. S. Polzik, A. Serafini, and M. M. Wolf, “Squeezing the limit: quantum benchmarks for the teleportation and storage of squeezed states,” New J. Phys. 10, 113014 (2008).
[CrossRef]

2007 (5)

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]

R. W. Boyd, K. W. Chan, and M. N. O’Sullivan, “Quantum weirdness in the lab,” Science 317, 1874–1875 (2007).
[CrossRef]

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (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 (2007).
[CrossRef]

M. G. Genoni, M. G. A. Paris, and K. Banaszek, “Measure of the non-Gaussian character of a quantum state,” Phys. Rev. A 76, 042327 (2007).
[CrossRef]

2006 (5)

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

F. Dell’Anno, S. De Siena, and F. Illuminati, “Multiphoton quantum optics and quantum state engineering,” Phys. Rep. 428, 53–168 (2006), and references therein.
[CrossRef]

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

H. Y. Fan, “Newton–Leibniz integration for ket–bra operators in quantum mechanics and derivation of entangled state representations,” Ann. Phys. 321, 480–494 (2006).
[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]

2005 (3)

N. Takei, H. Yonezawa, T. Aoki, and A. Furusawa, “High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continuous variables,” Phys. Rev. Lett. 94, 220502 (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]

S. Olivares and M. G. A. Paris, “Photon subtracted states and enhancement of nonlocality in the presence of noise,” J. Opt. B 7, S392–S397 (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]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).
[CrossRef]

X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

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

A. Kenfack and K. Zyczkowski, “Negativity of the Wigner function as an indicator of non-classicality,” J. Opt. B 6, 396–404 (2004).
[CrossRef]

2003 (4)

O. Glökl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[CrossRef]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, Hans-A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[CrossRef]

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A 67, 033802 (2003).
[CrossRef]

M. Matsuoka and T. Hirano, “Quantum key distribution with a single photon from a squeezed coherent state,” Phys. Rev. A 67, 042307 (2003).
[CrossRef]

2002 (1)

H. Y. Fan and Y. Fan, “Weyl ordering for entangled state representation,” Int. J. Mod. Phys. A 17, 701–708 (2002).
[CrossRef]

2001 (1)

D. Gottesman, A. Kitaev, and J. Preskill, “Encoding a qubit in an oscillator,” Phys. Rev. A 64, 012310 (2001).
[CrossRef]

1998 (1)

A. Furusawa, J. L. Søensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

1996 (1)

Z. Z. Xin, Y. B. Duan, H. M. Zhang, M. Hirayama, and K. Matumoto, “Excited two-photon coherent state of the radiation field,” J. Phys. B 29, 4493–4506 (1996).
[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]

1988 (1)

H. Fearn and M. J. Colletta, “Representations of squeezed states with thermal noise,” J. Mod. Opt. 35, 553–564 (1988).
[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]

1985 (1)

C. K. Hong and L. Mandel, “Generation of higher-order squeezing of quantum electromagnetic fields,” Phys. Rev. A 32, 974–982 (1985).
[CrossRef]

1932 (1)

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).
[CrossRef]

Agarwal, G. S.

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]

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]

Aoki, T.

N. Takei, H. Yonezawa, T. Aoki, and A. Furusawa, “High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continuous variables,” Phys. Rev. Lett. 94, 220502 (2005).
[CrossRef]

Aspachs, M.

J. Calsamiglia, M. Aspachs, R. Munoz-Tapia, and E. Bagan, “Phase-covariant quantum benchmarks,” Phys. Rev. A 79, 050301 (2009).
[CrossRef]

Bachor, Hans-A.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, Hans-A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[CrossRef]

Bagan, E.

J. Calsamiglia, M. Aspachs, R. Munoz-Tapia, and E. Bagan, “Phase-covariant quantum benchmarks,” Phys. Rev. A 79, 050301 (2009).
[CrossRef]

Banaszek, K.

M. G. Genoni, M. G. A. Paris, and K. Banaszek, “Quantifying the non-Gaussian character of a quantum state by quantum relative entropy,” Phys. Rev. A 78, 060303 (2008).
[CrossRef]

M. G. Genoni, M. G. A. Paris, and K. Banaszek, “Measure of the non-Gaussian character of a quantum state,” Phys. Rev. A 76, 042327 (2007).
[CrossRef]

Barbieri, M.

M. Barbieri, N. Spagnolo, M. G. Genoni, F. Ferreyrol, R. Blandino, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Non-Gaussianity of quantum states: an experimental test on single-photon-added coherent states,” Phys. Rev. A 82, 063833 (2010).
[CrossRef]

Bellini, M.

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]

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (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 (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]

Blandino, R.

M. Barbieri, N. Spagnolo, M. G. Genoni, F. Ferreyrol, R. Blandino, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Non-Gaussianity of quantum states: an experimental test on single-photon-added coherent states,” Phys. Rev. A 82, 063833 (2010).
[CrossRef]

Bowen, W. P.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, Hans-A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[CrossRef]

Boyd, R. W.

R. W. Boyd, K. W. Chan, and M. N. O’Sullivan, “Quantum weirdness in the lab,” Science 317, 1874–1875 (2007).
[CrossRef]

Braunstein, S. L.

A. Furusawa, J. L. Søensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

Brownnutt, M.

O. Glökl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[CrossRef]

Buchler, B. C.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, Hans-A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[CrossRef]

Calsamiglia, J.

J. Calsamiglia, M. Aspachs, R. Munoz-Tapia, and E. Bagan, “Phase-covariant quantum benchmarks,” Phys. Rev. A 79, 050301 (2009).
[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]

Chan, K. W.

R. W. Boyd, K. W. Chan, and M. N. O’Sullivan, “Quantum weirdness in the lab,” Science 317, 1874–1875 (2007).
[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]

Chou, C. W.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A 67, 033802 (2003).
[CrossRef]

Cirac, J. I.

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

Colletta, M. J.

H. Fearn and M. J. Colletta, “Representations of squeezed states with thermal noise,” J. Mod. Opt. 35, 553–564 (1988).
[CrossRef]

De Siena, S.

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M. G. Genoni and M. G. A. Paris, “Quantifying non-Gaussianity for quantum information,” Phys. Rev. A 82, 052341(2010).
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M. Barbieri, N. Spagnolo, M. G. Genoni, F. Ferreyrol, R. Blandino, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Non-Gaussianity of quantum states: an experimental test on single-photon-added coherent states,” Phys. Rev. A 82, 063833 (2010).
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M. Barbieri, N. Spagnolo, M. G. Genoni, F. Ferreyrol, R. Blandino, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Non-Gaussianity of quantum states: an experimental test on single-photon-added coherent states,” Phys. Rev. A 82, 063833 (2010).
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O. Glökl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
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Z. Z. Xin, Y. B. Duan, H. M. Zhang, M. Hirayama, and K. Matumoto, “Excited two-photon coherent state of the radiation field,” J. Phys. B 29, 4493–4506 (1996).
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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]

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).
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F. Dell’Anno, S. De Siena, and F. Illuminati, “Multiphoton quantum optics and quantum state engineering,” Phys. Rep. 428, 53–168 (2006), and references therein.
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K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nat. Phys. 7, 13–16 (2010).
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Kim, M.

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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).
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T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A 67, 033802 (2003).
[CrossRef]

A. Furusawa, J. L. Søensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

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D. Gottesman, A. Kitaev, and J. Preskill, “Encoding a qubit in an oscillator,” Phys. Rev. A 64, 012310 (2001).
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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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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).
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O. Glökl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
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K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nat. Phys. 7, 13–16 (2010).
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W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, Hans-A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
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A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
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Lee, S. Y.

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O. Glökl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
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O. Glökl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
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C. K. Hong and L. Mandel, “Generation of higher-order squeezing of quantum electromagnetic fields,” Phys. Rev. A 32, 974–982 (1985).
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O. Glökl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
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M. Matsuoka and T. Hirano, “Quantum key distribution with a single photon from a squeezed coherent state,” Phys. Rev. A 67, 042307 (2003).
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Z. Z. Xin, Y. B. Duan, H. M. Zhang, M. Hirayama, and K. Matumoto, “Excited two-photon coherent state of the radiation field,” J. Phys. B 29, 4493–4506 (1996).
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S. Olivares and M. G. A. Paris, “Photon subtracted states and enhancement of nonlocality in the presence of noise,” J. Opt. B 7, S392–S397 (2005).
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A. Ferraro, S. Olivares, and M. G. A. Paris, Gaussian States in Quantum Information (Bibliopolis, 2005).

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

Owari, M.

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nat. Phys. 7, 13–16 (2010).
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M. Owari, M. B. Plenio, E. S. Polzik, A. Serafini, and M. M. Wolf, “Squeezing the limit: quantum benchmarks for the teleportation and storage of squeezed states,” New J. Phys. 10, 113014 (2008).
[CrossRef]

Pan, Q.

X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

O. Glökl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[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 (2007).
[CrossRef]

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[CrossRef]

Paris, M. G. A.

M. G. Genoni and M. G. A. Paris, “Quantifying non-Gaussianity for quantum information,” Phys. Rev. A 82, 052341(2010).
[CrossRef]

M. Barbieri, N. Spagnolo, M. G. Genoni, F. Ferreyrol, R. Blandino, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Non-Gaussianity of quantum states: an experimental test on single-photon-added coherent states,” Phys. Rev. A 82, 063833 (2010).
[CrossRef]

M. G. Genoni, M. G. A. Paris, and K. Banaszek, “Quantifying the non-Gaussian character of a quantum state by quantum relative entropy,” Phys. Rev. A 78, 060303 (2008).
[CrossRef]

M. G. Genoni, M. G. A. Paris, and K. Banaszek, “Measure of the non-Gaussian character of a quantum state,” Phys. Rev. A 76, 042327 (2007).
[CrossRef]

S. Olivares and M. G. A. Paris, “Photon subtracted states and enhancement of nonlocality in the presence of noise,” J. Opt. B 7, S392–S397 (2005).
[CrossRef]

A. Ferraro, S. Olivares, and M. G. A. Paris, Gaussian States in Quantum Information (Bibliopolis, 2005).

Peng, K.

X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

Plenio, M. B.

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nat. Phys. 7, 13–16 (2010).
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M. Owari, M. B. Plenio, E. S. Polzik, A. Serafini, and M. M. Wolf, “Squeezing the limit: quantum benchmarks for the teleportation and storage of squeezed states,” New J. Phys. 10, 113014 (2008).
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Polzik, E. S.

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nat. Phys. 7, 13–16 (2010).
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M. Owari, M. B. Plenio, E. S. Polzik, A. Serafini, and M. M. Wolf, “Squeezing the limit: quantum benchmarks for the teleportation and storage of squeezed states,” New J. Phys. 10, 113014 (2008).
[CrossRef]

A. Furusawa, J. L. Søensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

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D. Gottesman, A. Kitaev, and J. Preskill, “Encoding a qubit in an oscillator,” Phys. Rev. A 64, 012310 (2001).
[CrossRef]

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R. R. Puri, Mathematical Methods of Quantum Optics (Springer-Verlag, 2001), Appendix A.

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W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, Hans-A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[CrossRef]

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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]

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W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, Hans-A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[CrossRef]

Serafini, A.

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nat. Phys. 7, 13–16 (2010).
[CrossRef]

M. Owari, M. B. Plenio, E. S. Polzik, A. Serafini, and M. M. Wolf, “Squeezing the limit: quantum benchmarks for the teleportation and storage of squeezed states,” New J. Phys. 10, 113014 (2008).
[CrossRef]

Silberhorn, C.

O. Glökl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[CrossRef]

Søensen, J. L.

A. Furusawa, J. L. Søensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

Spagnolo, N.

M. Barbieri, N. Spagnolo, M. G. Genoni, F. Ferreyrol, R. Blandino, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Non-Gaussianity of quantum states: an experimental test on single-photon-added coherent states,” Phys. Rev. A 82, 063833 (2010).
[CrossRef]

Su, X.

X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

Symul, T.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, Hans-A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[CrossRef]

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N. Takei, H. Yonezawa, T. Aoki, and A. Furusawa, “High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continuous variables,” Phys. Rev. Lett. 94, 220502 (2005).
[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]

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).
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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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W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, Hans-A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[CrossRef]

Tualle-Brouri, R.

M. Barbieri, N. Spagnolo, M. G. Genoni, F. Ferreyrol, R. Blandino, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Non-Gaussianity of quantum states: an experimental test on single-photon-added coherent states,” Phys. Rev. A 82, 063833 (2010).
[CrossRef]

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X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93, 250503 (2004).
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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).
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A. Ferraro, S. Olivares, and M. G. A. Paris, Gaussian States in Quantum Information (Bibliopolis, 2005).

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Figures (7)

Fig. 1.
Fig. 1.

Q parameter of the PADSTS as a function of the squeezing parameter r with given n¯=0.1 and ϕθ/2=π for some different values of m and |λ|. (a) |λ|=0.5 and (b) |λ|=2 (from top to bottom m=0, 1, 2, 3, 6).

Fig. 2.
Fig. 2.

Q parameter as a function of the compound phase ϕθ/2 in the range [0,2π] with given n¯=0.1, r=0.2 for (a) |λ|=0.5 and (b) |λ|=2 (m=0, 1, 2, 3, 6, 15, 20).

Fig. 3.
Fig. 3.

Degree of quadrature squeezing S as a function of the squeezing parameter r by setting ϕθ/2=π/2, for different values of displacement parameter and of the photon addition m. (a) |λ|=0.5, m=6, 3, 2, 1, 0 and (b) |λ|=2, m=0, 1, 2, 3, 6.

Fig. 4.
Fig. 4.

Degree of quadrature squeezing S as a function of ϕθ/2 with n¯=0.1, r=0.2, for different values of displacement parameter amplitude |λ| and of the photon addition m. (a) |λ|=0.5, m=6, 3, 2, 1, 15, 20, 0, and (b) |λ|=2, m=20, 0, 15, 1, 2, 3, 6.

Fig. 5.
Fig. 5.

WFs of the PADSTS with n¯=0.1, r=0.6, |λ|=0.5, ϕ=π/2, and θ=0. for (a) m=1 and (b) m=2. (c) and (d) are contour lines with interval 0.05, corresponding to (a) and (b), respectively, where only the negative regions are plotted.

Fig. 6.
Fig. 6.

(a) Fidelity between the PADSTS and the DSTS as a function of ϕθ/2 with n¯=0.1, r=0.3, and |λ|=0.5 for several different values of m=1, 2, 3 (from top to bottom lines). (b) Negative volume of the WFs of the PADSTS as a function of the compound phase ϕθ/2 with n¯=0.1, r=0.3, and |λ|=0.5 (from top to bottom lines m=3, 2, 1).

Fig. 7.
Fig. 7.

(a) Fidelity between the PADSTS and the DSTS as a function of the coherent amplitude |λ| with n¯=0.1, r=0.3, and ϕθ/2=π/2 for several different values of m=1, 2, 3 (from top to bottom lines). (b) Negative volume of the WFs of the PADSTS as a function of the coherent amplitude |λ| with n¯=0.1, r=0.3, and ϕθ/2=π/2 (from top to bottom lines m=3, 2, 1).

Equations (35)

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ρ=Nm1amρsam,
ρs=D(λ)S(ζ)ρcS1(ζ)D1(λ),
ρs=1μ:exp[υ(aλ)2+υ*(aλ*)2ω(aλ*)(aλ)]:,
μ=n¯2+(2n¯+1)cosh2r,
ω=n¯+(2n¯+1)cosh2rn¯2+(2n¯+1)cosh2r,
υ=14(2n¯+1)eiθsinh2rn¯2+(2n¯+1)cosh2r,
μ=1ω24|υ|2.
Nm=k=0m(μω)kk!|μυ|mk(m!)2[(mk)!]2|Hmk(iλ*2μυ)|2.
Nm,n¯=0=k=0mcosh2krk![m!(mk)!]2(sinh2r4)mk×|Hmk(λ*eiθ/2isinh2r)|2,
Ln(xy)=(1)nn!Hn,n(x,y)=(1)nn!2ntntnett+tx+ty|t=t=0.
Q=a2a2aaaa.
aa=Nm+1Nm1,
a2a2=Nm+2Nm4Nm+1Nm+2;
Q=Nm+24Nm+1+2NmNm+1NmNm+1NmNm.
S=2|a2a2|+2aa2|a|2,
a=Nm1km(iμυ*)(μω)kk!|μυ|mkm!(mk)!×(m+1)!(m+1k)!Hmk(iλ*2μυ)×Hm+1k(iλ2μυ*),
a2=Nm1km(iμυ*)2(μω)kk!|μυ|mkm!(mk)!×(m+2)!(m+2k)!Hmk(iλ*2μυ)×Hm+2k(iλ2μυ*).
S0=(2n¯+1)e2r1,
W(α,α*)=2e2|α|2πd2zπz|ρ|ze2(α*zαz*),
d2zπeζ|z|2+ξz+ηz*+fz2+gz*2=1ζ24fgeζξη+ξ2g+η2fζ24fg,
W(α,α*)=W0(α,α*)Nm2msmfmexp[Ωs+Ω*f+sinh2r4(2n+1)(eiθs2+eiθf2)n¯+cosh2r2n¯+1fs]f=s=0,
W0(α,α*)=2π(2n¯+1)exp[2cosh2r2n¯+1(|λ|2+|α|2)+sinh2r2n¯+1(eiθλ2+eiθλ*2+eiθα2+eiθα*2)+22n¯+1(α*cosh2reiθαsinh2r)λ+22n¯+1(αcosh2reiθα*sinh2r)λ*],
Ω=(λ*α*)eiθsinh2rλcosh2r+2α(n¯+cosh2r)2n¯+1.
Hn(x)=ntnexp(2xtt2)|t=0,
lxlHn(x)=2ln!(nl)!Hnl(x),
W(α,α*)=Γm(α,α*)W0(α,α*),
Γm(α,α*)=l=0m(1)lNml!(n¯+cosh2rsinh2r)l[(sinh2r)4(2n¯+1)]m×[2lm!(ml)!]2|Hml(i2n¯+1eiθsinh2rΩ)|2.
Γ1(α,α*)=N11(|Ω|2n¯+cosh2r2n¯+1).
Vm=12[d2α|W(α,α*)|1].
F=Tr(ρsρ)/Tr(ρs2).
Tr(ρs2)=Tr(ρc2)=12n¯+1.
Tr(ρsρ)=πd2αW0(α,α*)W(α,α*).
Tr(ρρs)=Nm12n¯+12msmfmexp[λs+λ*f+Δ(eiθs2+eiθf2)8n¯+4+cosh2r2n¯+1(n¯2+n¯)fs]f=s=0,
Fm=l=0m[(n¯2+n¯)cosh2r]lNml!(8n¯+4)m[2lm!(ml)!]2×(Δ)ml|Hml(iλeiθ/22n¯+1Δ)|2.
F1=N11(|λ|+(n¯2+n¯)cosh2r2n¯+1).

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