Abstract

We study the photon-number distributions (PND) of non-Gaussian states generated by subtracting m photons from or adding m photons to a displacement squeezed thermal state (DSTS). Compared with the PND of DSTS, PND of both m-photon-subtracted DSTS (PSDSTS) and m-photon-added DSTS (PADSTS) are modulated by a factor that is a monotonically increasing function of n, the photonnumber in the resulting non-Gaussian states. And the photon subtraction or addition essentially shifts the PND. We further demonstrate that both PND are periodic functions of the compound phase ϕθ/2 involved in complex squeezing and displacement parameters with a period π and exhibit more remarkable oscillations than that of DSTS. In the case of small squeezing and weak coherence, we investigate the negativity of Mandel’s Q parameter and the properties of PND of both PSDSTS and PADSTS. Our results indicate that generating new photon-number-controllable nonclassical states from a squeezed light with coherent component is effective by multiple-photon subtraction or addition when ϕθ/2=π/2.

© 2012 Optical Society of America

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    [CrossRef]
  32. 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).
  33. 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]
  34. 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]
  35. H. Y. Fan and Y. Fan “Weyl ordering for entangled state representation,” Int. J. Mod. Phys. A 17, 701–708 (2002).
    [CrossRef]
  36. H. Fearn and M. J. Colletta, “Representations of squeezed states with thermal noise,” J. Mod. Opt. 35, 553–564 (1988).
    [CrossRef]
  37. M. J. Collett, Ph.D. Thesis (University of Essex, 1987).
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    [CrossRef]
  39. R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
    [CrossRef]
  40. H. P. Yuen, “Two-photon coherent states of the radiation field,” Phys. Rev. A 13, 2226 (1976).
    [CrossRef]
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    [CrossRef]

2011 (1)

2010 (5)

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

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]

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).

H. Takahashi, J. S. Neergaard-Nielsenl, M. Takeuchil, M. Takeokal, K. Hayasakal, A. Furusawa, and M. Sasakil, “Entanglement distillation from Gaussian input states,” Nat. Photon. 4, 178–181 (2010).

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 (2)

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).

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]

2008 (2)

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

2007 (2)

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

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

2006 (4)

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).
[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]

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]

2005 (1)

J. Fiurrášek, R. Garcıa-Patroón, and N. J. Cerf, “Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions,” Phys. Rev. A 72033822 (2005).
[CrossRef]

2004 (1)

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

2003 (2)

S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleportation improvement by inconclusive photon subtraction,” Phys. Rev. A 67, 032314 (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 (2)

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

2000 (1)

T. Opatrny, 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]

1994 (1)

V. V. Dodonov, O. V. Man’ko, and V. I. Manko, “Photon distribution for one-mode mixed light with a generic Gaussian Wigner function,” Phys. Rev. A 49, 2993–3001 (1994).
[CrossRef]

1993 (1)

1992 (1)

P. Marian, “Higher-order squeezing and photon statistics for squeezed thermal states,” Phys. Rev. A 45, 2044–2051 (1992).
[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)

J. Peřina and J. Bajer, “Origin of oscillations in photon distributions of squeezed states,” Phys. Rev. A 41, 516–518 (1990).
[CrossRef]

1989 (3)

G. S. Agarwal and G. Adam, “Photon distributions for nonclassical fields with coherent components,” Phys. Rev. A 39, 6259–6266 (1989).
[CrossRef]

S. Chaturvedi and V. Srinivasan, “Photon-number distributions for fields with Gaussian Wigner functions,” Phys. Rev. A 40, 6095–6098 (1989).
[CrossRef]

M. S. Kim, F. A. M de Oliveira, and P. L. Knight, “Properties of squeezed number states and squeezed thermal states,” Phys. Rev. A 40, 2494–2503 (1989).
[CrossRef]

1988 (2)

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

W. Schleich, D. F. Walls, and J. A. Wheeler, “Area of overlap and interference in phase space versus Wigner pseudoprobabilities,” Phys. Rev. A 38, 1177–1186 (1988).
[CrossRef]

1987 (2)

W. Schleich and J. A. Wheeler, “Oscillations in photon distribution of squeezed states and interference in phase space,” Nature 326, 574–577 (1987).
[CrossRef]

W. Schleich and J. A. Wheeler, “Oscillations in photon distribution of squeezed states,” J. Opt. Soc. Am. B 4, 1715–1722 (1987).
[CrossRef]

1976 (1)

H. P. Yuen, “Two-photon coherent states of the radiation field,” Phys. Rev. A 13, 2226 (1976).
[CrossRef]

1963 (2)

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[CrossRef]

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[CrossRef]

Adam, G.

G. S. Agarwal and G. Adam, “Photon distributions for nonclassical fields with coherent components,” Phys. Rev. A 39, 6259–6266 (1989).
[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]

G. S. Agarwal and G. Adam, “Photon distributions for nonclassical fields with coherent components,” Phys. Rev. A 39, 6259–6266 (1989).
[CrossRef]

Albano, L.

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

Bajer, J.

J. Peřina and J. Bajer, “Origin of oscillations in photon distributions of squeezed states,” Phys. Rev. A 41, 516–518 (1990).
[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]

Bonifacio, R.

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

Boyd, R. W.

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

Carmichael, H. J.

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

Cerf, N. J.

J. Fiurrášek, R. Garcıa-Patroón, and N. J. Cerf, “Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions,” Phys. Rev. A 72033822 (2005).
[CrossRef]

Chan, K. W.

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

Chaturvedi, S.

S. Chaturvedi and V. Srinivasan, “Photon-number distributions for fields with Gaussian Wigner functions,” Phys. Rev. A 40, 6095–6098 (1989).
[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]

Cochrane, P. T.

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]

Collett, M. J.

M. J. Collett, Ph.D. Thesis (University of Essex, 1987).

Colletta, M. J.

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

Dainty, J. C.

J. C. Dainty, Current Trends in Optics (Academic, 1994), Vol. 2.

de Oliveira, F. A. M

M. S. Kim, F. A. M de Oliveira, and P. L. Knight, “Properties of squeezed number states and squeezed thermal states,” Phys. Rev. A 40, 2494–2503 (1989).
[CrossRef]

De Siena, S.

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

Dell’Anno, F.

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

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

DeSiena, S.

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

Dodonov, V. V.

V. V. Dodonov, O. V. Man’ko, and V. I. Manko, “Photon distribution for one-mode mixed light with a generic Gaussian Wigner function,” Phys. Rev. A 49, 2993–3001 (1994).
[CrossRef]

Dutta, B.

Fan, H. Y.

S. Wang, X. X. Xu, H. C. Yuan, L. Y. Hu, and H. Y. Fan, “Coherent operation of photon subtraction and addition for squeezed thermal states: analysis of nonclassicality and decoherence,” J. Opt. Soc. Am. B 28, 2149–2152 (2011).
[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]

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]

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]

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]

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

Fan, Y.

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

Fearn, H.

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

Fiurrášek, J.

J. Fiurrášek, R. Garcıa-Patroón, and N. J. Cerf, “Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions,” Phys. Rev. A 72033822 (2005).
[CrossRef]

Furusawa, A.

H. Takahashi, J. S. Neergaard-Nielsenl, M. Takeuchil, M. Takeokal, K. Hayasakal, A. Furusawa, and M. Sasakil, “Entanglement distillation from Gaussian input states,” Nat. Photon. 4, 178–181 (2010).

Garcia-Patroón, R.

J. Fiurrášek, R. Garcıa-Patroón, and N. J. Cerf, “Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions,” Phys. Rev. A 72033822 (2005).
[CrossRef]

Glauber, R. J.

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[CrossRef]

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[CrossRef]

Grangier, P.

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

Grangier, Ph.

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

Hayasakal, K.

H. Takahashi, J. S. Neergaard-Nielsenl, M. Takeuchil, M. Takeokal, K. Hayasakal, A. Furusawa, and M. Sasakil, “Entanglement distillation from Gaussian input states,” Nat. Photon. 4, 178–181 (2010).

Hirano, T.

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

Hu, L. Y.

S. Wang, X. X. Xu, H. C. Yuan, L. Y. Hu, and H. Y. Fan, “Coherent operation of photon subtraction and addition for squeezed thermal states: analysis of nonclassicality and decoherence,” J. Opt. Soc. Am. B 28, 2149–2152 (2011).
[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]

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).

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]

Illuminati, F.

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

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

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]

M. S. Kim, F. A. M de Oliveira, and P. L. Knight, “Properties of squeezed number states and squeezed thermal states,” Phys. Rev. A 40, 2494–2503 (1989).
[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]

Knight, P. L.

M. S. Kim, F. A. M de Oliveira, and P. L. Knight, “Properties of squeezed number states and squeezed thermal states,” Phys. Rev. A 40, 2494–2503 (1989).
[CrossRef]

Kurizki, G.

T. Opatrny, 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]

Laurat, J.

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

Lee, S. Y.

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

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).

Man’ko, O. V.

V. V. Dodonov, O. V. Man’ko, and V. I. Manko, “Photon distribution for one-mode mixed light with a generic Gaussian Wigner function,” Phys. Rev. A 49, 2993–3001 (1994).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University, 1995).

Manko, V. I.

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[CrossRef]

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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]

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Neergaard-Nielsenl, J. S.

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Nha, H.

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

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[CrossRef]

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T. Opatrny, 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]

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[CrossRef]

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[CrossRef]

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

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J. Peřina and J. Bajer, “Origin of oscillations in photon distributions of squeezed states,” Phys. Rev. A 41, 516–518 (1990).
[CrossRef]

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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]

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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]

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H. Takahashi, J. S. Neergaard-Nielsenl, M. Takeuchil, M. Takeokal, K. Hayasakal, A. Furusawa, and M. Sasakil, “Entanglement distillation from Gaussian input states,” Nat. Photon. 4, 178–181 (2010).

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Takahashi, H.

H. Takahashi, J. S. Neergaard-Nielsenl, M. Takeuchil, M. Takeokal, K. Hayasakal, A. Furusawa, and M. Sasakil, “Entanglement distillation from Gaussian input states,” Nat. Photon. 4, 178–181 (2010).

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]

Takeokal, M.

H. Takahashi, J. S. Neergaard-Nielsenl, M. Takeuchil, M. Takeokal, K. Hayasakal, A. Furusawa, and M. Sasakil, “Entanglement distillation from Gaussian input states,” Nat. Photon. 4, 178–181 (2010).

Takeuchil, M.

H. Takahashi, J. S. Neergaard-Nielsenl, M. Takeuchil, M. Takeokal, K. Hayasakal, A. Furusawa, and M. Sasakil, “Entanglement distillation from Gaussian input states,” Nat. Photon. 4, 178–181 (2010).

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J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).
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W. Schleich, D. F. Walls, and J. A. Wheeler, “Area of overlap and interference in phase space versus Wigner pseudoprobabilities,” Phys. Rev. A 38, 1177–1186 (1988).
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Welsch, D.-G.

T. Opatrny, G. Kurizki, and D.-G. Welsch, “ Improvement on teleportation of continuous variables by photon subtraction via conditional measurement,” Phys. Rev. A 61, 032302(2000).
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J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (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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Nature (1)

W. Schleich and J. A. Wheeler, “Oscillations in photon distribution of squeezed states and interference in phase space,” Nature 326, 574–577 (1987).
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Opt. Commun. (1)

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).
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[CrossRef]

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[CrossRef]

W. Schleich, D. F. Walls, and J. A. Wheeler, “Area of overlap and interference in phase space versus Wigner pseudoprobabilities,” Phys. Rev. A 38, 1177–1186 (1988).
[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]

T. Opatrny, 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]

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

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[CrossRef]

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[CrossRef]

J. Peřina and J. Bajer, “Origin of oscillations in photon distributions of squeezed states,” Phys. Rev. A 41, 516–518 (1990).
[CrossRef]

P. Marian, “Higher-order squeezing and photon statistics for squeezed thermal states,” Phys. Rev. A 45, 2044–2051 (1992).
[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).

V. V. Dodonov, O. V. Man’ko, and V. I. Manko, “Photon distribution for one-mode mixed light with a generic Gaussian Wigner function,” Phys. Rev. A 49, 2993–3001 (1994).
[CrossRef]

Phys. Rev. Lett. (2)

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

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

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]

Science (2)

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

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

Other (4)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University, 1995).

M. J. Collett, Ph.D. Thesis (University of Essex, 1987).

J. C. Dainty, Current Trends in Optics (Academic, 1994), Vol. 2.

W. P. Schleich, Quantum Optics in Phase Space (Wiley-VCH, 2001).

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Figures (8)

Fig. 1.
Fig. 1.

Photon-number distributions of DSTS with n¯=1, |α|=0.5, and λ=3 for (a) ϕθ/2=0, (b)   ϕθ/2=π/6, (c) ϕθ/2=π/3, and (d) ϕθ/2=π/2. (Blue bars represent the even photon-number distribution, while red bars indicate odd photon-number distribution).

Fig. 2.
Fig. 2.

Photon-number distributions of PSDSTS with n=0.1, λ=2, ϕθ/2=π/2, and |α|=0.5 for (a) m=0, (b) m=1, (c) m=2, and (d) m=5. (Blue line represents the even photon-number distribution, while red dot line indicates odd photon-number distribution).

Fig. 3.
Fig. 3.

Photon-number distributions of PSDSTS with n¯=0, λ=2, |α|=0.5, and ϕθ/2=π/2 for (a) m=0, (b) m=1, (c) m=2, and (d) m=5.

Fig. 4.
Fig. 4.

Photon-number distributions of PSDSTS with n=0.1, λ=2, ϕθ/2=π/2, and m=3 for (a) |α|=0, (b) |α|=1, and (c) |α|=3.

Fig. 5.
Fig. 5.

Photon-number distributions with given λ=2, n=0.1, ϕθ/2=π/2, |α|=0.5 and m=3, for (a) in the case of PSDSTS, (b) in the case of PADSTS, and (c) the difference between PSDSTS and PADSTS, i.e., ΔP(n)=Ps(n)Pa(n).

Fig. 6.
Fig. 6.

Mandel’s Q parameter as function of squeezing parameter with given n=0.0 for different m. For PSDSTS with |α|=0.5 (a) ϕθ/2=0 and (b) ϕθ/2=π/2; for PADSTS with |α|=0.3 (c) ϕθ/2=0 and (d) ϕθ/2=π/2 (except Fig. 6(b), from top to bottom lines m=0, 1, 3, 6).

Fig. 7.
Fig. 7.

Photon-number distributions of PSDSTS with n=0.0, λ=0.1, and |α|=0.5 for ϕθ/2=0 (a) m=1, (b) m=3, (c) m=6, and for ϕθ/2=π/2 (d) m=1, (e) m=3, (f) m=6.

Fig. 8.
Fig. 8.

Photon-number distributions of PADSTS with n=0.0, λ=0.09, and |α|=0.3 for ϕθ/2=0 (a) m=1, (b) m=3, (c) m=6, and for ϕθ/2=π/2 (d) m=1, (e) m=3, (f) m=6.

Equations (32)

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

ρDST=D(α)S(ζ)ρTS1(ζ)D1(α),
ρDST=1μexp[υ(aα)2+υ*(aα*)2ω(aα*)(aα)],
μ=n¯2+(2n¯+1)cosh2λ,
ω=n¯+(2n¯+1)cosh2λn¯2+(2n¯+1)cosh2λ,
υ=14(2n¯+1)eiθ sinh2λn2+(2n¯+1)cosh2λ,
μ=1ω24|υ|2.
P(n)=Tr{ρ|nn|},
P(n)=1n!dndz2*ndndz1nz2|ρDST|z1z1=z2=0=exp[B]n!μdndz2*ndndz1nexp[Az1+A*z2*+υz12+υ*z2*2(ω1)z1z2*]z1=z2=0,
A=ωα*2υα,
B=υα2+υ*α*2ω|α|2.
P(n)=exp[B]n!μdndz2*ndndz1nl=0(1ω)ll!2lAlA*l×exp[Az1+υz12+A*z2*+υ*z2*2]|z1=z2=0=|υ|nexp[B]n!μl=0(1ω)ll!|lAlHn(iA2υ)|2.
Hn(x)=ntnexp[2xtt2]|t=0.
lxlHn(x)=2ln!(nl)!Hnl(x),
P(n)=exp[υα2+υ*α*2ω|α|2]μ×l=0nn!(1ω)l|υ|nll![(nl)!]2|Hnl(ωα*2υα2iυ)|2.
P(n)=tanhnλ2nn!coshλexp[tanhλ2(eiθα2+eiθα*2)|α|2]×|Hn(eiθ/2α*coshλeiθ/2αsinhλisinh2λ)|2.
ρs=Cm1amρDSTam,
Cm=k=0m(μω1)kk!|μυ|mk[m!(mk)!]2×|Hmk(α*2iμυ)|2,
Ps(n)=(m+n)!Cm1n!μm+n|exp[υ(aα)2+υ*(aα*)2ω(aα*)(aα)]|m+n.
Ps(n)=exp[B]Cmn!μdm+ndz2*m+ndm+ndz1m+nexp[Az1+A*z2*+υz12+υ*z2*2(ω1)z1z2*]|z1=z2=0=|υ|m+nexp[B]Cmn!μl=0(1ω)ll!|lAlHn+m(iA2υ)|2.
Ps(n)=Cm1(n+m)!n!P(n+m),
Ps(n)=Cm1(n+m)!n!P(n+m),
Cm,n¯=0=k=0msinh2kλk![m!(mk)!]2|sinh2λ4|mk×|Hmk(α*eiθ/2isinh2λ)|2.
ρa=Nm1amρDSTam,
Nm=k=0m(μω)kk!|μυ|mk[m!(mk)!]2|Hmk(iα*2μυ)|2,
ρa=Nm1μamexp[υ(aα)2+υ*(aα*)2ω(aα*)(aα)]am.
Pa(n)=n|ρa|n=exp[υα2+υ*α*2ω|α|2]Nmn!μdndz2*ndndz1nz2*mz1mexp[(2υα+ωα*)z1+(2υ*α*+ωα)z2*+υz12+υ*z2*2(ω1)z1z2*]z1=z2=0.
{Pa(n)=Nm1n!(nm)!P(nm),nmPa(n)=0,n<m,
{Pa(n)=Nm,n=01n!(nm)!P(nm),nmPa(n)=0,n<m,
Nm,n¯=0=k=0mcosh2kλk![m!(mk)!]2|sinh2λ4|mk×|Hmk(α*eiθ/2isinh2λ)|2.
Q=a2a2aaaa,
Qs=Cm+2Cm+1Cm+1Cm.
Qa=Nm+24Nm+1+2NmNm+1NmNm+1NmNm.

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