Abstract

A quantum illumination protocol exploits correlated light beams to enhance the probability of detection of a partially reflecting object lying in a very noisy background. Recently a simple photon-number-detection-based implementation of a quantum illumination-like scheme was provided in Phys. Rev. Lett. 101, 153603 (2013), where the enhancement was preserved despite the loss of nonclassicality. In the present paper, we investigate the source for quantum advantage in that realization. We introduce an effective two-mode description of the light sources and analyze the mutual information (MI) as a quantifier of total correlations in the effective two-mode picture. In the relevant regime of a highly thermalized background, we find that the improvement in the signal-to-noise ratio achieved by the entangled sources over the unentangled thermal ones amounts exactly to the ratio of the effective MIs of the corresponding sources. More precisely, both quantities tend to a common limit specified by the squared ratio of the respective cross correlations. A thorough analysis of the experimental data confirms this theoretical result.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
    [CrossRef]
  4. N. Thomas-Peter, B. J. Smith, A. Datta, L. Zhang, U. Dorner, and I. A. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107, 113603 (2011).
    [CrossRef]
  5. C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
    [CrossRef]
  6. S. Olivares, “Quantum optics in the phase space: a tutorial on Gaussian states,” Eur. Phys. J. Spec. Top. 203, 3–24 (2012).
    [CrossRef]
  7. G. Adesso, S. Ragy, and A. Lee, “Continuous variable quantum information: Gaussian states and beyond,” Open Syst. Inf. Dyn. 21, 1440001 (2014).
    [CrossRef]
  8. Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein–Podolsky–Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. G. Brida, M. Genovese, and I. Ruo-Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
    [CrossRef]
  24. G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
    [CrossRef]
  25. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
    [CrossRef]
  26. S. Ragy is preparing a manuscript to be called “A Gaussian single mode approximation for multi-mode photon counting statistics.”
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    [CrossRef]
  30. S. Ragy and G. Adesso, “Unveiling the Hanbury Brown and Twiss effect through Renyi entropy correlations,” Phys. Scr. T153, 014052 (2013).
    [CrossRef]
  31. E. D. Lopaeva, I. R. Berchera, S. Olivares, G. Brida, I. P. Degiovanni, and M. Genovese, “A detailed description of the experimental realisation of quantum illumination protocol,” Phys. Scr. T160, 014026 (2014).
    [CrossRef]
  32. M. Bondani, A. Allevi, G. Zambda, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
    [CrossRef]
  33. T. Ishkakov, M. V. Checkhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
    [CrossRef]
  34. M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. K. Lam, “Observing the operational significance of discord consumption,” Nat. Phys. 8, 671–675 (2012).
    [CrossRef]

2014

G. Adesso, S. Ragy, and A. Lee, “Continuous variable quantum information: Gaussian states and beyond,” Open Syst. Inf. Dyn. 21, 1440001 (2014).
[CrossRef]

D. Girolami, A. M. Souza, V. Giovannetti, T. Tufarelli, J. G. Filgueiras, R. S. Sarthour, D. O. Soares-Pinto, I. S. Oliveira, and G. Adesso, “Quantum discord determines the interferometric power of quantum states,” Phys. Rev. Lett. 112, 210401 (2014).
[CrossRef]

A. Farace, A. De Pasquale, L. Rigovacca, and V. Giovannetti, “Discriminating strength: a bona fide measure of non-classical correlations,” New J. Phys. 16, 073010 (2014).

E. D. Lopaeva, I. R. Berchera, S. Olivares, G. Brida, I. P. Degiovanni, and M. Genovese, “A detailed description of the experimental realisation of quantum illumination protocol,” Phys. Scr. T160, 014026 (2014).
[CrossRef]

2013

S. Ragy and G. Adesso, “Unveiling the Hanbury Brown and Twiss effect through Renyi entropy correlations,” Phys. Scr. T153, 014052 (2013).
[CrossRef]

T. Eberle, V. Händchen, and R. Schnabel, “Stable control of 10  dB two-mode squeezed vacuum states of light,” Opt. Express 21, 11546 (2013).
[CrossRef]

E. D. Lopaeva, I. R. Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[CrossRef]

Z. Zhang, M. Tengner, T. Zhong, F. N. C. Wong, and J. H. Shapiro, “Entanglement’s benefit survives an entanglement-breaking channel,” Phys. Rev. Lett. 111, 010501 (2013).
[CrossRef]

2012

C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

S. Olivares, “Quantum optics in the phase space: a tutorial on Gaussian states,” Eur. Phys. J. Spec. Top. 203, 3–24 (2012).
[CrossRef]

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. K. Lam, “Observing the operational significance of discord consumption,” Nat. Phys. 8, 671–675 (2012).
[CrossRef]

G. Adesso, D. Girolami, and A. Serafini, “Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2,” Phys. Rev. Lett. 109, 190502 (2012).
[CrossRef]

S. Ragy and G. Adesso, “Nature of light correlations in ghost imaging,” Sci. Rep. 2, 651 (2012).
[CrossRef]

2011

N. Thomas-Peter, B. J. Smith, A. Datta, L. Zhang, U. Dorner, and I. A. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107, 113603 (2011).
[CrossRef]

S. Olivares and M. G. A. Paris, “Fidelity matters: the birth of entanglement in the mixing of Gaussian states,” Phys. Rev. Lett. 107, 170505 (2011).
[CrossRef]

2010

G. Brida, M. Genovese, and I. Ruo-Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[CrossRef]

2009

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef]

T. Ishkakov, M. V. Checkhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[CrossRef]

V. D’Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, “Full characterization of Gaussian bipartite entangled states by a single homodyne detector,” Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef]

S. Guha and B. I. Erkmen, “Gaussian-state quantum-illumination receivers for target detection,” Phys. Rev. A 80, 052310 (2009).
[CrossRef]

T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[CrossRef]

2008

S. Lloyd, “Enhanced sensitivity of photodetection via quantum illumination,” Science 321, 1463–1465 (2008).
[CrossRef]

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[CrossRef]

S. Pirandola and S. Lloyd, “Computable bounds for the discrimination of Gaussian states,” Phys. Rev. A 78, 012331 (2008).
[CrossRef]

2007

K. M. R. Audenaert, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, “Discriminating states: the quantum Chernoff bound,” Phys. Rev. Lett. 98, 160501 (2007).
[CrossRef]

G. Adesso and F. Illuminati, “Entanglement in continuous-variable systems: recent advances and current perspectives,” J. Phys. A Math. Theor. 40, 7821–7880 (2007).
[CrossRef]

M. Bondani, A. Allevi, G. Zambda, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

2005

J. Laurat, G. Keller, J. A. Oliveira-Huguenin, C. Fabre, T. Coudreau, A. Serafini, G. Adesso, and F. Illuminati, “Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation,” J. Opt. B 7, S577–S587 (2005).
[CrossRef]

2004

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

1992

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein–Podolsky–Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[CrossRef]

Acin, A.

K. M. R. Audenaert, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, “Discriminating states: the quantum Chernoff bound,” Phys. Rev. Lett. 98, 160501 (2007).
[CrossRef]

Adesso, G.

G. Adesso, S. Ragy, and A. Lee, “Continuous variable quantum information: Gaussian states and beyond,” Open Syst. Inf. Dyn. 21, 1440001 (2014).
[CrossRef]

D. Girolami, A. M. Souza, V. Giovannetti, T. Tufarelli, J. G. Filgueiras, R. S. Sarthour, D. O. Soares-Pinto, I. S. Oliveira, and G. Adesso, “Quantum discord determines the interferometric power of quantum states,” Phys. Rev. Lett. 112, 210401 (2014).
[CrossRef]

S. Ragy and G. Adesso, “Unveiling the Hanbury Brown and Twiss effect through Renyi entropy correlations,” Phys. Scr. T153, 014052 (2013).
[CrossRef]

S. Ragy and G. Adesso, “Nature of light correlations in ghost imaging,” Sci. Rep. 2, 651 (2012).
[CrossRef]

G. Adesso, D. Girolami, and A. Serafini, “Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2,” Phys. Rev. Lett. 109, 190502 (2012).
[CrossRef]

G. Adesso and F. Illuminati, “Entanglement in continuous-variable systems: recent advances and current perspectives,” J. Phys. A Math. Theor. 40, 7821–7880 (2007).
[CrossRef]

J. Laurat, G. Keller, J. A. Oliveira-Huguenin, C. Fabre, T. Coudreau, A. Serafini, G. Adesso, and F. Illuminati, “Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation,” J. Opt. B 7, S577–S587 (2005).
[CrossRef]

G. Adesso, “Gaussian interferometric power,” arXiv:1406.5857 (2014).

Allevi, A.

M. Bondani, A. Allevi, G. Zambda, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

Andreoni, A.

M. Bondani, A. Allevi, G. Zambda, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

Assad, S. M.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. K. Lam, “Observing the operational significance of discord consumption,” Nat. Phys. 8, 671–675 (2012).
[CrossRef]

Audenaert, K. M. R.

K. M. R. Audenaert, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, “Discriminating states: the quantum Chernoff bound,” Phys. Rev. Lett. 98, 160501 (2007).
[CrossRef]

Bache, M.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Bagan, E.

K. M. R. Audenaert, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, “Discriminating states: the quantum Chernoff bound,” Phys. Rev. Lett. 98, 160501 (2007).
[CrossRef]

Berchera, I. R.

E. D. Lopaeva, I. R. Berchera, S. Olivares, G. Brida, I. P. Degiovanni, and M. Genovese, “A detailed description of the experimental realisation of quantum illumination protocol,” Phys. Scr. T160, 014026 (2014).
[CrossRef]

E. D. Lopaeva, I. R. Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[CrossRef]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef]

Bondani, M.

M. Bondani, A. Allevi, G. Zambda, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

Brambilla, E.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Brida, G.

E. D. Lopaeva, I. R. Berchera, S. Olivares, G. Brida, I. P. Degiovanni, and M. Genovese, “A detailed description of the experimental realisation of quantum illumination protocol,” Phys. Scr. T160, 014026 (2014).
[CrossRef]

E. D. Lopaeva, I. R. Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[CrossRef]

G. Brida, M. Genovese, and I. Ruo-Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[CrossRef]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef]

Calsamiglia, J.

K. M. R. Audenaert, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, “Discriminating states: the quantum Chernoff bound,” Phys. Rev. Lett. 98, 160501 (2007).
[CrossRef]

Caspani, L.

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef]

Cerf, N. J.

C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

Checkhova, M. V.

T. Ishkakov, M. V. Checkhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[CrossRef]

Chekhova, M. V.

T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[CrossRef]

Chrzanowski, H. M.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. K. Lam, “Observing the operational significance of discord consumption,” Nat. Phys. 8, 671–675 (2012).
[CrossRef]

Coudreau, T.

J. Laurat, G. Keller, J. A. Oliveira-Huguenin, C. Fabre, T. Coudreau, A. Serafini, G. Adesso, and F. Illuminati, “Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation,” J. Opt. B 7, S577–S587 (2005).
[CrossRef]

D’Auria, V.

V. D’Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, “Full characterization of Gaussian bipartite entangled states by a single homodyne detector,” Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef]

Datta, A.

N. Thomas-Peter, B. J. Smith, A. Datta, L. Zhang, U. Dorner, and I. A. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107, 113603 (2011).
[CrossRef]

De Pasquale, A.

A. Farace, A. De Pasquale, L. Rigovacca, and V. Giovannetti, “Discriminating strength: a bona fide measure of non-classical correlations,” New J. Phys. 16, 073010 (2014).

Degiovanni, I. P.

E. D. Lopaeva, I. R. Berchera, S. Olivares, G. Brida, I. P. Degiovanni, and M. Genovese, “A detailed description of the experimental realisation of quantum illumination protocol,” Phys. Scr. T160, 014026 (2014).
[CrossRef]

E. D. Lopaeva, I. R. Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[CrossRef]

Dorner, U.

N. Thomas-Peter, B. J. Smith, A. Datta, L. Zhang, U. Dorner, and I. A. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107, 113603 (2011).
[CrossRef]

Eberle, T.

Erkmen, B. I.

S. Guha and B. I. Erkmen, “Gaussian-state quantum-illumination receivers for target detection,” Phys. Rev. A 80, 052310 (2009).
[CrossRef]

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[CrossRef]

Fabre, C.

J. Laurat, G. Keller, J. A. Oliveira-Huguenin, C. Fabre, T. Coudreau, A. Serafini, G. Adesso, and F. Illuminati, “Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation,” J. Opt. B 7, S577–S587 (2005).
[CrossRef]

Farace, A.

A. Farace, A. De Pasquale, L. Rigovacca, and V. Giovannetti, “Discriminating strength: a bona fide measure of non-classical correlations,” New J. Phys. 16, 073010 (2014).

Filgueiras, J. G.

D. Girolami, A. M. Souza, V. Giovannetti, T. Tufarelli, J. G. Filgueiras, R. S. Sarthour, D. O. Soares-Pinto, I. S. Oliveira, and G. Adesso, “Quantum discord determines the interferometric power of quantum states,” Phys. Rev. Lett. 112, 210401 (2014).
[CrossRef]

Fornaro, S.

V. D’Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, “Full characterization of Gaussian bipartite entangled states by a single homodyne detector,” Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef]

Garcia-Patron, R.

C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

Gatti, A.

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Genovese, M.

E. D. Lopaeva, I. R. Berchera, S. Olivares, G. Brida, I. P. Degiovanni, and M. Genovese, “A detailed description of the experimental realisation of quantum illumination protocol,” Phys. Scr. T160, 014026 (2014).
[CrossRef]

E. D. Lopaeva, I. R. Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[CrossRef]

G. Brida, M. Genovese, and I. Ruo-Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[CrossRef]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef]

Giovannetti, V.

D. Girolami, A. M. Souza, V. Giovannetti, T. Tufarelli, J. G. Filgueiras, R. S. Sarthour, D. O. Soares-Pinto, I. S. Oliveira, and G. Adesso, “Quantum discord determines the interferometric power of quantum states,” Phys. Rev. Lett. 112, 210401 (2014).
[CrossRef]

A. Farace, A. De Pasquale, L. Rigovacca, and V. Giovannetti, “Discriminating strength: a bona fide measure of non-classical correlations,” New J. Phys. 16, 073010 (2014).

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[CrossRef]

Girolami, D.

D. Girolami, A. M. Souza, V. Giovannetti, T. Tufarelli, J. G. Filgueiras, R. S. Sarthour, D. O. Soares-Pinto, I. S. Oliveira, and G. Adesso, “Quantum discord determines the interferometric power of quantum states,” Phys. Rev. Lett. 112, 210401 (2014).
[CrossRef]

G. Adesso, D. Girolami, and A. Serafini, “Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2,” Phys. Rev. Lett. 109, 190502 (2012).
[CrossRef]

Gu, M.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. K. Lam, “Observing the operational significance of discord consumption,” Nat. Phys. 8, 671–675 (2012).
[CrossRef]

C. Weedbrook, S. Pirandola, J. Thompson, V. Vedral, and M. Gu, “Discord empowered quantum illumination,” arXiv:1312.3332 (2013).

Guha, S.

S. Guha and B. I. Erkmen, “Gaussian-state quantum-illumination receivers for target detection,” Phys. Rev. A 80, 052310 (2009).
[CrossRef]

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[CrossRef]

Händchen, V.

Illuminati, F.

G. Adesso and F. Illuminati, “Entanglement in continuous-variable systems: recent advances and current perspectives,” J. Phys. A Math. Theor. 40, 7821–7880 (2007).
[CrossRef]

J. Laurat, G. Keller, J. A. Oliveira-Huguenin, C. Fabre, T. Coudreau, A. Serafini, G. Adesso, and F. Illuminati, “Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation,” J. Opt. B 7, S577–S587 (2005).
[CrossRef]

Ishkakov, T.

T. Ishkakov, M. V. Checkhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[CrossRef]

Iskhakov, T.

T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[CrossRef]

Keller, G.

J. Laurat, G. Keller, J. A. Oliveira-Huguenin, C. Fabre, T. Coudreau, A. Serafini, G. Adesso, and F. Illuminati, “Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation,” J. Opt. B 7, S577–S587 (2005).
[CrossRef]

Kimble, H. J.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein–Podolsky–Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[CrossRef]

Lam, P. K.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. K. Lam, “Observing the operational significance of discord consumption,” Nat. Phys. 8, 671–675 (2012).
[CrossRef]

Laurat, J.

J. Laurat, G. Keller, J. A. Oliveira-Huguenin, C. Fabre, T. Coudreau, A. Serafini, G. Adesso, and F. Illuminati, “Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation,” J. Opt. B 7, S577–S587 (2005).
[CrossRef]

Lee, A.

G. Adesso, S. Ragy, and A. Lee, “Continuous variable quantum information: Gaussian states and beyond,” Open Syst. Inf. Dyn. 21, 1440001 (2014).
[CrossRef]

Leuchs, G.

T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[CrossRef]

T. Ishkakov, M. V. Checkhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[CrossRef]

Lloyd, S.

C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

S. Lloyd, “Enhanced sensitivity of photodetection via quantum illumination,” Science 321, 1463–1465 (2008).
[CrossRef]

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[CrossRef]

S. Pirandola and S. Lloyd, “Computable bounds for the discrimination of Gaussian states,” Phys. Rev. A 78, 012331 (2008).
[CrossRef]

Lopaeva, E. D.

E. D. Lopaeva, I. R. Berchera, S. Olivares, G. Brida, I. P. Degiovanni, and M. Genovese, “A detailed description of the experimental realisation of quantum illumination protocol,” Phys. Scr. T160, 014026 (2014).
[CrossRef]

E. D. Lopaeva, I. R. Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[CrossRef]

Lugiato, L. A.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Maccone, L.

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[CrossRef]

Masanes, L.

K. M. R. Audenaert, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, “Discriminating states: the quantum Chernoff bound,” Phys. Rev. Lett. 98, 160501 (2007).
[CrossRef]

Meda, A.

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef]

Modi, K.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. K. Lam, “Observing the operational significance of discord consumption,” Nat. Phys. 8, 671–675 (2012).
[CrossRef]

Munoz-Tapia, R.

K. M. R. Audenaert, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, “Discriminating states: the quantum Chernoff bound,” Phys. Rev. Lett. 98, 160501 (2007).
[CrossRef]

Olivares, S.

E. D. Lopaeva, I. R. Berchera, S. Olivares, G. Brida, I. P. Degiovanni, and M. Genovese, “A detailed description of the experimental realisation of quantum illumination protocol,” Phys. Scr. T160, 014026 (2014).
[CrossRef]

E. D. Lopaeva, I. R. Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[CrossRef]

S. Olivares, “Quantum optics in the phase space: a tutorial on Gaussian states,” Eur. Phys. J. Spec. Top. 203, 3–24 (2012).
[CrossRef]

S. Olivares and M. G. A. Paris, “Fidelity matters: the birth of entanglement in the mixing of Gaussian states,” Phys. Rev. Lett. 107, 170505 (2011).
[CrossRef]

V. D’Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, “Full characterization of Gaussian bipartite entangled states by a single homodyne detector,” Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef]

Oliveira, I. S.

D. Girolami, A. M. Souza, V. Giovannetti, T. Tufarelli, J. G. Filgueiras, R. S. Sarthour, D. O. Soares-Pinto, I. S. Oliveira, and G. Adesso, “Quantum discord determines the interferometric power of quantum states,” Phys. Rev. Lett. 112, 210401 (2014).
[CrossRef]

Oliveira-Huguenin, J. A.

J. Laurat, G. Keller, J. A. Oliveira-Huguenin, C. Fabre, T. Coudreau, A. Serafini, G. Adesso, and F. Illuminati, “Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation,” J. Opt. B 7, S577–S587 (2005).
[CrossRef]

Ou, Z. Y.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein–Podolsky–Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[CrossRef]

Paris, M. G. A.

S. Olivares and M. G. A. Paris, “Fidelity matters: the birth of entanglement in the mixing of Gaussian states,” Phys. Rev. Lett. 107, 170505 (2011).
[CrossRef]

V. D’Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, “Full characterization of Gaussian bipartite entangled states by a single homodyne detector,” Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef]

M. Bondani, A. Allevi, G. Zambda, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

Peng, K. C.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein–Podolsky–Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[CrossRef]

Pereira, S. F.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein–Podolsky–Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[CrossRef]

Pirandola, S.

C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[CrossRef]

S. Pirandola and S. Lloyd, “Computable bounds for the discrimination of Gaussian states,” Phys. Rev. A 78, 012331 (2008).
[CrossRef]

C. Weedbrook, S. Pirandola, J. Thompson, V. Vedral, and M. Gu, “Discord empowered quantum illumination,” arXiv:1312.3332 (2013).

Porzio, A.

V. D’Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, “Full characterization of Gaussian bipartite entangled states by a single homodyne detector,” Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef]

Ragy, S.

G. Adesso, S. Ragy, and A. Lee, “Continuous variable quantum information: Gaussian states and beyond,” Open Syst. Inf. Dyn. 21, 1440001 (2014).
[CrossRef]

S. Ragy and G. Adesso, “Unveiling the Hanbury Brown and Twiss effect through Renyi entropy correlations,” Phys. Scr. T153, 014052 (2013).
[CrossRef]

S. Ragy and G. Adesso, “Nature of light correlations in ghost imaging,” Sci. Rep. 2, 651 (2012).
[CrossRef]

S. Ragy is preparing a manuscript to be called “A Gaussian single mode approximation for multi-mode photon counting statistics.”

Ralph, T. C.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. K. Lam, “Observing the operational significance of discord consumption,” Nat. Phys. 8, 671–675 (2012).
[CrossRef]

C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

Rényi, A.

A. Rényi, “On measures of entropy and information,” in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (University of California, 1961), Vol. 1, pp. 547–561.

Rigovacca, L.

A. Farace, A. De Pasquale, L. Rigovacca, and V. Giovannetti, “Discriminating strength: a bona fide measure of non-classical correlations,” New J. Phys. 16, 073010 (2014).

Ruo-Berchera, I.

G. Brida, M. Genovese, and I. Ruo-Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[CrossRef]

Sarthour, R. S.

D. Girolami, A. M. Souza, V. Giovannetti, T. Tufarelli, J. G. Filgueiras, R. S. Sarthour, D. O. Soares-Pinto, I. S. Oliveira, and G. Adesso, “Quantum discord determines the interferometric power of quantum states,” Phys. Rev. Lett. 112, 210401 (2014).
[CrossRef]

Schnabel, R.

Serafini, A.

G. Adesso, D. Girolami, and A. Serafini, “Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2,” Phys. Rev. Lett. 109, 190502 (2012).
[CrossRef]

J. Laurat, G. Keller, J. A. Oliveira-Huguenin, C. Fabre, T. Coudreau, A. Serafini, G. Adesso, and F. Illuminati, “Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation,” J. Opt. B 7, S577–S587 (2005).
[CrossRef]

Shapiro, J. H.

Z. Zhang, M. Tengner, T. Zhong, F. N. C. Wong, and J. H. Shapiro, “Entanglement’s benefit survives an entanglement-breaking channel,” Phys. Rev. Lett. 111, 010501 (2013).
[CrossRef]

C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[CrossRef]

Smith, B. J.

N. Thomas-Peter, B. J. Smith, A. Datta, L. Zhang, U. Dorner, and I. A. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107, 113603 (2011).
[CrossRef]

Soares-Pinto, D. O.

D. Girolami, A. M. Souza, V. Giovannetti, T. Tufarelli, J. G. Filgueiras, R. S. Sarthour, D. O. Soares-Pinto, I. S. Oliveira, and G. Adesso, “Quantum discord determines the interferometric power of quantum states,” Phys. Rev. Lett. 112, 210401 (2014).
[CrossRef]

Solimeno, S.

V. D’Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, “Full characterization of Gaussian bipartite entangled states by a single homodyne detector,” Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef]

Souza, A. M.

D. Girolami, A. M. Souza, V. Giovannetti, T. Tufarelli, J. G. Filgueiras, R. S. Sarthour, D. O. Soares-Pinto, I. S. Oliveira, and G. Adesso, “Quantum discord determines the interferometric power of quantum states,” Phys. Rev. Lett. 112, 210401 (2014).
[CrossRef]

Symul, T.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. K. Lam, “Observing the operational significance of discord consumption,” Nat. Phys. 8, 671–675 (2012).
[CrossRef]

Tan, S.-H.

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[CrossRef]

Tengner, M.

Z. Zhang, M. Tengner, T. Zhong, F. N. C. Wong, and J. H. Shapiro, “Entanglement’s benefit survives an entanglement-breaking channel,” Phys. Rev. Lett. 111, 010501 (2013).
[CrossRef]

Thomas-Peter, N.

N. Thomas-Peter, B. J. Smith, A. Datta, L. Zhang, U. Dorner, and I. A. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107, 113603 (2011).
[CrossRef]

Thompson, J.

C. Weedbrook, S. Pirandola, J. Thompson, V. Vedral, and M. Gu, “Discord empowered quantum illumination,” arXiv:1312.3332 (2013).

Tufarelli, T.

D. Girolami, A. M. Souza, V. Giovannetti, T. Tufarelli, J. G. Filgueiras, R. S. Sarthour, D. O. Soares-Pinto, I. S. Oliveira, and G. Adesso, “Quantum discord determines the interferometric power of quantum states,” Phys. Rev. Lett. 112, 210401 (2014).
[CrossRef]

Vedral, V.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. K. Lam, “Observing the operational significance of discord consumption,” Nat. Phys. 8, 671–675 (2012).
[CrossRef]

C. Weedbrook, S. Pirandola, J. Thompson, V. Vedral, and M. Gu, “Discord empowered quantum illumination,” arXiv:1312.3332 (2013).

Verstraete, F.

K. M. R. Audenaert, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, “Discriminating states: the quantum Chernoff bound,” Phys. Rev. Lett. 98, 160501 (2007).
[CrossRef]

Walmsley, I. A.

N. Thomas-Peter, B. J. Smith, A. Datta, L. Zhang, U. Dorner, and I. A. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107, 113603 (2011).
[CrossRef]

Weedbrook, C.

C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

C. Weedbrook, S. Pirandola, J. Thompson, V. Vedral, and M. Gu, “Discord empowered quantum illumination,” arXiv:1312.3332 (2013).

Wong, F. N. C.

Z. Zhang, M. Tengner, T. Zhong, F. N. C. Wong, and J. H. Shapiro, “Entanglement’s benefit survives an entanglement-breaking channel,” Phys. Rev. Lett. 111, 010501 (2013).
[CrossRef]

Zambda, G.

M. Bondani, A. Allevi, G. Zambda, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

Zhang, L.

N. Thomas-Peter, B. J. Smith, A. Datta, L. Zhang, U. Dorner, and I. A. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107, 113603 (2011).
[CrossRef]

Zhang, Z.

Z. Zhang, M. Tengner, T. Zhong, F. N. C. Wong, and J. H. Shapiro, “Entanglement’s benefit survives an entanglement-breaking channel,” Phys. Rev. Lett. 111, 010501 (2013).
[CrossRef]

Zhong, T.

Z. Zhang, M. Tengner, T. Zhong, F. N. C. Wong, and J. H. Shapiro, “Entanglement’s benefit survives an entanglement-breaking channel,” Phys. Rev. Lett. 111, 010501 (2013).
[CrossRef]

Eur. Phys. J. Spec. Top.

S. Olivares, “Quantum optics in the phase space: a tutorial on Gaussian states,” Eur. Phys. J. Spec. Top. 203, 3–24 (2012).
[CrossRef]

J. Opt. B

J. Laurat, G. Keller, J. A. Oliveira-Huguenin, C. Fabre, T. Coudreau, A. Serafini, G. Adesso, and F. Illuminati, “Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation,” J. Opt. B 7, S577–S587 (2005).
[CrossRef]

J. Phys. A Math. Theor.

G. Adesso and F. Illuminati, “Entanglement in continuous-variable systems: recent advances and current perspectives,” J. Phys. A Math. Theor. 40, 7821–7880 (2007).
[CrossRef]

Nat. Photonics

G. Brida, M. Genovese, and I. Ruo-Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[CrossRef]

Nat. Phys.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. K. Lam, “Observing the operational significance of discord consumption,” Nat. Phys. 8, 671–675 (2012).
[CrossRef]

New J. Phys.

A. Farace, A. De Pasquale, L. Rigovacca, and V. Giovannetti, “Discriminating strength: a bona fide measure of non-classical correlations,” New J. Phys. 16, 073010 (2014).

Open Syst. Inf. Dyn.

G. Adesso, S. Ragy, and A. Lee, “Continuous variable quantum information: Gaussian states and beyond,” Open Syst. Inf. Dyn. 21, 1440001 (2014).
[CrossRef]

Opt. Express

Phys. Rev. A

S. Pirandola and S. Lloyd, “Computable bounds for the discrimination of Gaussian states,” Phys. Rev. A 78, 012331 (2008).
[CrossRef]

S. Guha and B. I. Erkmen, “Gaussian-state quantum-illumination receivers for target detection,” Phys. Rev. A 80, 052310 (2009).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

M. Bondani, A. Allevi, G. Zambda, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

Phys. Rev. Lett.

T. Ishkakov, M. V. Checkhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[CrossRef]

G. Adesso, D. Girolami, and A. Serafini, “Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2,” Phys. Rev. Lett. 109, 190502 (2012).
[CrossRef]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef]

E. D. Lopaeva, I. R. Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, “Experimental realization of quantum illumination,” Phys. Rev. Lett. 110, 153603 (2013).
[CrossRef]

Z. Zhang, M. Tengner, T. Zhong, F. N. C. Wong, and J. H. Shapiro, “Entanglement’s benefit survives an entanglement-breaking channel,” Phys. Rev. Lett. 111, 010501 (2013).
[CrossRef]

S. Olivares and M. G. A. Paris, “Fidelity matters: the birth of entanglement in the mixing of Gaussian states,” Phys. Rev. Lett. 107, 170505 (2011).
[CrossRef]

K. M. R. Audenaert, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, “Discriminating states: the quantum Chernoff bound,” Phys. Rev. Lett. 98, 160501 (2007).
[CrossRef]

D. Girolami, A. M. Souza, V. Giovannetti, T. Tufarelli, J. G. Filgueiras, R. S. Sarthour, D. O. Soares-Pinto, I. S. Oliveira, and G. Adesso, “Quantum discord determines the interferometric power of quantum states,” Phys. Rev. Lett. 112, 210401 (2014).
[CrossRef]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein–Podolsky–Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[CrossRef]

V. D’Auria, S. Fornaro, A. Porzio, S. Solimeno, S. Olivares, and M. G. A. Paris, “Full characterization of Gaussian bipartite entangled states by a single homodyne detector,” Phys. Rev. Lett. 102, 020502 (2009).
[CrossRef]

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum illumination with Gaussian states,” Phys. Rev. Lett. 101, 253601 (2008).
[CrossRef]

T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[CrossRef]

N. Thomas-Peter, B. J. Smith, A. Datta, L. Zhang, U. Dorner, and I. A. Walmsley, “Real-world quantum sensors: evaluating resources for precision measurement,” Phys. Rev. Lett. 107, 113603 (2011).
[CrossRef]

Phys. Scr.

S. Ragy and G. Adesso, “Unveiling the Hanbury Brown and Twiss effect through Renyi entropy correlations,” Phys. Scr. T153, 014052 (2013).
[CrossRef]

E. D. Lopaeva, I. R. Berchera, S. Olivares, G. Brida, I. P. Degiovanni, and M. Genovese, “A detailed description of the experimental realisation of quantum illumination protocol,” Phys. Scr. T160, 014026 (2014).
[CrossRef]

Rev. Mod. Phys.

C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

Sci. Rep.

S. Ragy and G. Adesso, “Nature of light correlations in ghost imaging,” Sci. Rep. 2, 651 (2012).
[CrossRef]

Science

S. Lloyd, “Enhanced sensitivity of photodetection via quantum illumination,” Science 321, 1463–1465 (2008).
[CrossRef]

Other

S. Ragy is preparing a manuscript to be called “A Gaussian single mode approximation for multi-mode photon counting statistics.”

A. Rényi, “On measures of entropy and information,” in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (University of California, 1961), Vol. 1, pp. 547–561.

G. Adesso, “Gaussian interferometric power,” arXiv:1406.5857 (2014).

C. Weedbrook, S. Pirandola, J. Thompson, V. Vedral, and M. Gu, “Discord empowered quantum illumination,” arXiv:1312.3332 (2013).

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Figures (3)

Fig. 1.
Fig. 1.

Schematic diagram of a quantum illumination scheme. Here the object under consideration is a beam splitter. A portion of the light produced by the correlated source will be reflected by the beam splitter, and the challenge is to detect this beneath the dominant thermal noise, thereby discriminating the presence of the object.

Fig. 2.
Fig. 2.

Theoretical plot of the ratios RSNR (blue solid) and RMI (red dashed) for quantum illumination with parameters set at realistic experimental values of N=4000, M=90000, Mβ=50, η=0.38, and ηβ=0.5. The asymptotic limit for Nβ is given by Eq. (7).

Fig. 3.
Fig. 3.

(a)–(d) Experimental results and theoretical expectations for the SNRs (blue solid lines) and effective MIs (red dashed lines) of the quantum illumination demonstration of Lopaeva et al. [16] using TWB and THB light, plotted versus the bath photon number Nβ. The values of the other experimental parameters are fixed at M=90000, Mβ=1300, η=0.38, ηβ=0.5, NTWB=4232, NTHB=3278, for all the plots in this figure. (e) Ratios R˜ between SNR and MI for TWB (magenta empty squares) and THB (green filled triangles) sources, obtained from the measured data; the dashed gray curve represents the theoretical prediction, given by the mean between R˜TWB and R˜THB. (f) Confidence intervals (shadings) inferred from the experimental data, along with theoretical predictions (lines), for the ratios RSNR (blue solid) and RMI (red dashed).

Equations (15)

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SNR=|ΔinΔout|δ2Δin+δ2Δout
a^eff=1M+Mβk=1M+Mβa^k,
σkj=Tr[ρ^(R^kR^j+R^jR^k)].
MI(r:s)=S2(ρr)+S2(ρs)S2(ρrs).
σS=(aS0cS00aS0dScS0bS00dS0bS),
aTHB=aTWB=1+2ημ1,
bTHB=bTWB=1+ημ1M+2ηβμβMβM+Mβ,
cTHB=dTHB=ημ12MM+Mβ,
cTWB=dTWB=ημ12+μ12MM+Mβ,
RSNR=SNRTWBSNRTHB,
RMI=MITWBMITHB.
limNβRSNR=limNβRMI=|cTWBcTHB|2,
RSNR|ΔinΔout|TWB|ΔinΔout|THB.
RSNRSNRTWBSNRTHBMITWBMITHBRMI,
R˜TWBSNRTWBMITWBSNRTHBMITHBR˜THB,

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