Abstract

We report an investigation on quantum discord in classical second-order interference. In particular, we theoretically show that a bipartite state with D = 0.311 of discord can be generated via classical second-order interference. We also experimentally verify the theory by obtaining D = 0.197 ± 0.060 of non-zero discord state. Together with the fact that the nonclassicalities originated from physical constraints and information theoretic perspectives are not equivalent, this result provides an insight to understand the nature of quantum discord.

© 2017 Optical Society of America

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  27. S. Hamieh, R. Kobes, and H. Zaraket, “Positive-operator-valued measure optimization of classical correlations,” Phys. Rev. A 70, 052325 (2004).
    [Crossref]
  28. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044 (1987).
    [Crossref] [PubMed]
  29. Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett 61, 2921 (1998).
    [Crossref]
  30. H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011).
    [Crossref] [PubMed]
  31. J. G. Rarity, P. R. Tapster, and R. Loudon, “Non-classical interference between independent sources,” J. Opt. B: Quantum Semiclass. Opt. 7, S171 (2005).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  36. M. S. Kim, W. Son, V. Bužek, and P. L. Knight, “Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement,” Phys. Rev. A 65, 032323 (2002).
    [Crossref]
  37. X.-B. Wang, “Theorem for the beam-splitter entangler,” Phys. Rev. A 66, 024303 (2002).
    [Crossref]
  38. J.-C. Lee, Y.-C. Jeong, Y.-S. Kim, and Y.-H. Kim, “Experimental demonstration of decoherence suppression via quantum measurement reversal,” Opt. Express 19, 16309 (2011).
    [Crossref] [PubMed]
  39. Y.-S. Kim, J-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nat. Phys. 8, 117 (2012).
    [Crossref]
  40. K. Banaszek, G. M. D’Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (1999).
    [Crossref]
  41. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
    [Crossref]
  42. B. K. Park, Y.-S. Kim, O. Kwon, S.-W. Han, and S. Moon, “High-performance reconfigurable coincidence counting unit based on a field programmable gate array,” Appl. Opt. 54, 4727 (2015).
    [Crossref] [PubMed]
  43. C. Benedetti, A. P. Shurupov, M. G. A. Paris, G. Brida, and M. Genovese, “Experimental estimation of quantum discord for a polarization qubit and the use of fidelity to assess quantum correlations,” Phys. Rev. A 87, 052136 (2013).
    [Crossref]
  44. A. Mandarino, M. Bina, C. Porto, S. Cialdi, S. Olivares, and M. G. A. Paris, “Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems,” Phys. Rev. A 93, 062118 (2016).
    [Crossref]

2016 (1)

A. Mandarino, M. Bina, C. Porto, S. Cialdi, S. Olivares, and M. G. A. Paris, “Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems,” Phys. Rev. A 93, 062118 (2016).
[Crossref]

2015 (4)

B. K. Park, Y.-S. Kim, O. Kwon, S.-W. Han, and S. Moon, “High-performance reconfigurable coincidence counting unit based on a field programmable gate array,” Appl. Opt. 54, 4727 (2015).
[Crossref] [PubMed]

J. Yune, K.-H. Hong, H.-T. Lim, J.-C. Lee, O. Kwon, S.-W. Han, Y.-S. Kim, S. Moon, and Y.-H. Kim, “Quantum discord protection from amplitude damping decoherence,” Opt. Express 23, 26012 (2015).
[Crossref] [PubMed]

V. Chille, N. Quinn, C. Peuntinger, C. Croal, L. Mista, C. Marquardt, G. Leuches, and N. Korolkova, “Quantum nature of Gaussian discord: Experimental evidence and role of system-environment correlations,” Phys. Rev. A 91, 050301 (2015).
[Crossref]

L. Zhang, A. K. Pati, and J. Wu, “Interference visibility, entanglement, and quantum correlation,” Phys. Rev. A 92, 022316 (2015).
[Crossref]

2014 (5)

S. Hosseini, S. Rahimi-Keshari, J. Y. Haw, S. M. Assad, H. M. Chrzanowski, J. Janousek, T. Symul, T. C. Ralph, and P. K. Lam, “Experimental verification of quantum discord in continuous-variable states,” J. Phys. B: At. Mol. Opt. Phys. 47, 025503 (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]

M. P. Almeida, M. Gu, A. Fedrizzi, M. A. Broome, T. C. Ralph, and A. G. White, “Entanglement-free certification of entangling gates,” Phys. Rev. A 89, 042323 (2014).
[Crossref]

S. Pirandola, “Quantum discord as a resource for quantum cryptography,” Sci. Rep. 4, 6956 (2014).
[Crossref] [PubMed]

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Two-photon interference with continuous-wave multi-mode coherent light,” Opt. Express 22, 3611 (2014).
[Crossref] [PubMed]

2013 (3)

C. Benedetti, A. P. Shurupov, M. G. A. Paris, G. Brida, and M. Genovese, “Experimental estimation of quantum discord for a polarization qubit and the use of fidelity to assess quantum correlations,” Phys. Rev. A 87, 052136 (2013).
[Crossref]

A. Meda, S. Olivares, I. P. Degiovanni, G. Brida, M. Genovese, and M. G. A. Paris, “Revealing interference by continuous variable discordant states,” Opt. Lett. 38, 3099–3102 (2013).
[Crossref] [PubMed]

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

2012 (5)

A. Ferraro and M. G. A. Paris, “Nonclassicality criteria from phase-space representations and information-theoretical constraints are maximally inequivalent,” Phys. Rev. Lett. 108, 260403 (2012).
[Crossref] [PubMed]

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Homodyne estimation of Gaussian quantum discord,” Phys. Rev. Lett. 109, 180402 (2012).
[Crossref] [PubMed]

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: Discord and related measures,” Rev. Mod. Phys. 84, 1655 (2012).
[Crossref]

B. Dakic, Y.O. Lipp, X.S. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, C. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
[Crossref]

Y.-S. Kim, J-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nat. Phys. 8, 117 (2012).
[Crossref]

2011 (3)

J.-C. Lee, Y.-C. Jeong, Y.-S. Kim, and Y.-H. Kim, “Experimental demonstration of decoherence suppression via quantum measurement reversal,” Opt. Express 19, 16309 (2011).
[Crossref] [PubMed]

K. Modi, H. Cable, M. Williamson, and V. Vedral, “Quantum correlations in mixed-state metrology,” Phys. Rev. X 1, 021022 (2011).

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011).
[Crossref] [PubMed]

2010 (4)

J.-S. Xu, X.-Y. Xu, C.-F. Li, C.-J. Zhang, X.-B. Zou, and G.-C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Comm. 1, 7 (2010).
[Crossref]

L. Mazzola, J. Piilo, and S. Maniscalco, “Sudden transition between classical and quantum decoherence,” Phys. Rev. Lett. 104, 200401 (2010).
[Crossref] [PubMed]

A. Brodutch and D. R. Terno, “Quantum discord, local operations, and Maxwell’s demons,” Phys. Rev. A 81, 062103 (2010).
[Crossref]

A. Ferraro, L. Aolita, D. Cavalcanti, F. M. Cucchietti, and A. Acín, “Almost all quantum states have nonclassical correlations,” Phys. Rev. A 81, 052318 (2010).
[Crossref]

2009 (2)

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865 (2009).
[Crossref]

A. Shabani and D. A. Lidar, “Vanishing quantum discord is necessary and sufficient for completely positive maps,” Phys. Rev. Lett. 102, 100402 (2009).
[Crossref] [PubMed]

2008 (2)

A. Datta, A. Shaji, and C. M. Caves, “Quantum discord and the power of one qubit,” Phys. Rev. Lett. 100, 050502 (2008).
[Crossref] [PubMed]

B. P. Lanyon, M. Barbieri, M. P. Almeida, and A. G. White, “Experimental quantum computing without entanglement,” Phys. Rev. Lett. 101, 200501 (2008).
[Crossref] [PubMed]

2006 (1)

J. Niset and N. J. Cerf, “Multipartite nonlocality without entanglement in many dimensions,” Phys. Rev. A 74, 052103 (2006).
[Crossref]

2005 (2)

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus nonlocal information in quantum-information theory: Formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[Crossref]

J. G. Rarity, P. R. Tapster, and R. Loudon, “Non-classical interference between independent sources,” J. Opt. B: Quantum Semiclass. Opt. 7, S171 (2005).
[Crossref]

2004 (1)

S. Hamieh, R. Kobes, and H. Zaraket, “Positive-operator-valued measure optimization of classical correlations,” Phys. Rev. A 70, 052325 (2004).
[Crossref]

2003 (1)

W. H. Zurek, “Quantum discord and Maxwell’s demons,” Phys. Rev. A 67, 012320 (2003).
[Crossref]

2002 (2)

M. S. Kim, W. Son, V. Bužek, and P. L. Knight, “Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement,” Phys. Rev. A 65, 032323 (2002).
[Crossref]

X.-B. Wang, “Theorem for the beam-splitter entangler,” Phys. Rev. A 66, 024303 (2002).
[Crossref]

2001 (3)

L. Henderson and V. Vedral, “Classical, quantum and total correlations,” J. Phys. A: Math. Gen. 34, 6899 (2001).
[Crossref]

H. Ollivier and W.H. Zurek, “Quantum discord: A measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
[Crossref]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[Crossref]

1999 (2)

K. Banaszek, G. M. D’Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (1999).
[Crossref]

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070 (1999).
[Crossref]

1998 (2)

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245 (1998).
[Crossref]

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett 61, 2921 (1998).
[Crossref]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044 (1987).
[Crossref] [PubMed]

Acín, A.

A. Ferraro, L. Aolita, D. Cavalcanti, F. M. Cucchietti, and A. Acín, “Almost all quantum states have nonclassical correlations,” Phys. Rev. A 81, 052318 (2010).
[Crossref]

Adesso, 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]

Alley, C. O.

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett 61, 2921 (1998).
[Crossref]

Almeida, M. P.

M. P. Almeida, M. Gu, A. Fedrizzi, M. A. Broome, T. C. Ralph, and A. G. White, “Entanglement-free certification of entangling gates,” Phys. Rev. A 89, 042323 (2014).
[Crossref]

B. P. Lanyon, M. Barbieri, M. P. Almeida, and A. G. White, “Experimental quantum computing without entanglement,” Phys. Rev. Lett. 101, 200501 (2008).
[Crossref] [PubMed]

Aolita, L.

A. Ferraro, L. Aolita, D. Cavalcanti, F. M. Cucchietti, and A. Acín, “Almost all quantum states have nonclassical correlations,” Phys. Rev. A 81, 052318 (2010).
[Crossref]

Assad, S. M.

S. Hosseini, S. Rahimi-Keshari, J. Y. Haw, S. M. Assad, H. M. Chrzanowski, J. Janousek, T. Symul, T. C. Ralph, and P. K. Lam, “Experimental verification of quantum discord in continuous-variable states,” J. Phys. B: At. Mol. Opt. Phys. 47, 025503 (2014).
[Crossref]

Bae, J.

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011).
[Crossref] [PubMed]

Banaszek, K.

K. Banaszek, G. M. D’Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (1999).
[Crossref]

Barbieri, M.

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Homodyne estimation of Gaussian quantum discord,” Phys. Rev. Lett. 109, 180402 (2012).
[Crossref] [PubMed]

B. P. Lanyon, M. Barbieri, M. P. Almeida, and A. G. White, “Experimental quantum computing without entanglement,” Phys. Rev. Lett. 101, 200501 (2008).
[Crossref] [PubMed]

Barz, S.

B. Dakic, Y.O. Lipp, X.S. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, C. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
[Crossref]

Benedetti, C.

C. Benedetti, A. P. Shurupov, M. G. A. Paris, G. Brida, and M. Genovese, “Experimental estimation of quantum discord for a polarization qubit and the use of fidelity to assess quantum correlations,” Phys. Rev. A 87, 052136 (2013).
[Crossref]

Bennett, C. H.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070 (1999).
[Crossref]

Bina, M.

A. Mandarino, M. Bina, C. Porto, S. Cialdi, S. Olivares, and M. G. A. Paris, “Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems,” Phys. Rev. A 93, 062118 (2016).
[Crossref]

Blandino, R.

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Homodyne estimation of Gaussian quantum discord,” Phys. Rev. Lett. 109, 180402 (2012).
[Crossref] [PubMed]

Brida, G.

A. Meda, S. Olivares, I. P. Degiovanni, G. Brida, M. Genovese, and M. G. A. Paris, “Revealing interference by continuous variable discordant states,” Opt. Lett. 38, 3099–3102 (2013).
[Crossref] [PubMed]

C. Benedetti, A. P. Shurupov, M. G. A. Paris, G. Brida, and M. Genovese, “Experimental estimation of quantum discord for a polarization qubit and the use of fidelity to assess quantum correlations,” Phys. Rev. A 87, 052136 (2013).
[Crossref]

Brodutch, A.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: Discord and related measures,” Rev. Mod. Phys. 84, 1655 (2012).
[Crossref]

A. Brodutch and D. R. Terno, “Quantum discord, local operations, and Maxwell’s demons,” Phys. Rev. A 81, 062103 (2010).
[Crossref]

Broome, M. A.

M. P. Almeida, M. Gu, A. Fedrizzi, M. A. Broome, T. C. Ralph, and A. G. White, “Entanglement-free certification of entangling gates,” Phys. Rev. A 89, 042323 (2014).
[Crossref]

Brukner, C.

B. Dakic, Y.O. Lipp, X.S. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, C. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
[Crossref]

Bužek, V.

M. S. Kim, W. Son, V. Bužek, and P. L. Knight, “Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement,” Phys. Rev. A 65, 032323 (2002).
[Crossref]

Cable, H.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: Discord and related measures,” Rev. Mod. Phys. 84, 1655 (2012).
[Crossref]

K. Modi, H. Cable, M. Williamson, and V. Vedral, “Quantum correlations in mixed-state metrology,” Phys. Rev. X 1, 021022 (2011).

Cavalcanti, D.

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V. Chille, N. Quinn, C. Peuntinger, C. Croal, L. Mista, C. Marquardt, G. Leuches, and N. Korolkova, “Quantum nature of Gaussian discord: Experimental evidence and role of system-environment correlations,” Phys. Rev. A 91, 050301 (2015).
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S. Hosseini, S. Rahimi-Keshari, J. Y. Haw, S. M. Assad, H. M. Chrzanowski, J. Janousek, T. Symul, T. C. Ralph, and P. K. Lam, “Experimental verification of quantum discord in continuous-variable states,” J. Phys. B: At. Mol. Opt. Phys. 47, 025503 (2014).
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A. Mandarino, M. Bina, C. Porto, S. Cialdi, S. Olivares, and M. G. A. Paris, “Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems,” Phys. Rev. A 93, 062118 (2016).
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V. Chille, N. Quinn, C. Peuntinger, C. Croal, L. Mista, C. Marquardt, G. Leuches, and N. Korolkova, “Quantum nature of Gaussian discord: Experimental evidence and role of system-environment correlations,” Phys. Rev. A 91, 050301 (2015).
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B. Dakic, Y.O. Lipp, X.S. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, C. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
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DiVincenzo, D. P.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070 (1999).
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R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Homodyne estimation of Gaussian quantum discord,” Phys. Rev. Lett. 109, 180402 (2012).
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M. P. Almeida, M. Gu, A. Fedrizzi, M. A. Broome, T. C. Ralph, and A. G. White, “Entanglement-free certification of entangling gates,” Phys. Rev. A 89, 042323 (2014).
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A. Ferraro and M. G. A. Paris, “Nonclassicality criteria from phase-space representations and information-theoretical constraints are maximally inequivalent,” Phys. Rev. Lett. 108, 260403 (2012).
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A. Ferraro, L. Aolita, D. Cavalcanti, F. M. Cucchietti, and A. Acín, “Almost all quantum states have nonclassical correlations,” Phys. Rev. A 81, 052318 (2010).
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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).
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C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070 (1999).
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R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Homodyne estimation of Gaussian quantum discord,” Phys. Rev. Lett. 109, 180402 (2012).
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A. Meda, S. Olivares, I. P. Degiovanni, G. Brida, M. Genovese, and M. G. A. Paris, “Revealing interference by continuous variable discordant states,” Opt. Lett. 38, 3099–3102 (2013).
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C. Benedetti, A. P. Shurupov, M. G. A. Paris, G. Brida, and M. Genovese, “Experimental estimation of quantum discord for a polarization qubit and the use of fidelity to assess quantum correlations,” Phys. Rev. A 87, 052136 (2013).
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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).
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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).
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R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Homodyne estimation of Gaussian quantum discord,” Phys. Rev. Lett. 109, 180402 (2012).
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M. P. Almeida, M. Gu, A. Fedrizzi, M. A. Broome, T. C. Ralph, and A. G. White, “Entanglement-free certification of entangling gates,” Phys. Rev. A 89, 042323 (2014).
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J.-S. Xu, X.-Y. Xu, C.-F. Li, C.-J. Zhang, X.-B. Zou, and G.-C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Comm. 1, 7 (2010).
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S. Hamieh, R. Kobes, and H. Zaraket, “Positive-operator-valued measure optimization of classical correlations,” Phys. Rev. A 70, 052325 (2004).
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Haw, J. Y.

S. Hosseini, S. Rahimi-Keshari, J. Y. Haw, S. M. Assad, H. M. Chrzanowski, J. Janousek, T. Symul, T. C. Ralph, and P. K. Lam, “Experimental verification of quantum discord in continuous-variable states,” J. Phys. B: At. Mol. Opt. Phys. 47, 025503 (2014).
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M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus nonlocal information in quantum-information theory: Formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
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M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus nonlocal information in quantum-information theory: Formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
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S. Hosseini, S. Rahimi-Keshari, J. Y. Haw, S. M. Assad, H. M. Chrzanowski, J. Janousek, T. Symul, T. C. Ralph, and P. K. Lam, “Experimental verification of quantum discord in continuous-variable states,” J. Phys. B: At. Mol. Opt. Phys. 47, 025503 (2014).
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S. Hosseini, S. Rahimi-Keshari, J. Y. Haw, S. M. Assad, H. M. Chrzanowski, J. Janousek, T. Symul, T. C. Ralph, and P. K. Lam, “Experimental verification of quantum discord in continuous-variable states,” J. Phys. B: At. Mol. Opt. Phys. 47, 025503 (2014).
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H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011).
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Kim, Y.-H.

Kim, Y.-S.

Knight, P. L.

M. S. Kim, W. Son, V. Bužek, and P. L. Knight, “Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement,” Phys. Rev. A 65, 032323 (2002).
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S. Hamieh, R. Kobes, and H. Zaraket, “Positive-operator-valued measure optimization of classical correlations,” Phys. Rev. A 70, 052325 (2004).
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V. Chille, N. Quinn, C. Peuntinger, C. Croal, L. Mista, C. Marquardt, G. Leuches, and N. Korolkova, “Quantum nature of Gaussian discord: Experimental evidence and role of system-environment correlations,” Phys. Rev. A 91, 050301 (2015).
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B. Dakic, Y.O. Lipp, X.S. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, C. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
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D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
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Kwon, O.

Lam, P. K.

S. Hosseini, S. Rahimi-Keshari, J. Y. Haw, S. M. Assad, H. M. Chrzanowski, J. Janousek, T. Symul, T. C. Ralph, and P. K. Lam, “Experimental verification of quantum discord in continuous-variable states,” J. Phys. B: At. Mol. Opt. Phys. 47, 025503 (2014).
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V. Chille, N. Quinn, C. Peuntinger, C. Croal, L. Mista, C. Marquardt, G. Leuches, and N. Korolkova, “Quantum nature of Gaussian discord: Experimental evidence and role of system-environment correlations,” Phys. Rev. A 91, 050301 (2015).
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Li, C.-F.

J.-S. Xu, X.-Y. Xu, C.-F. Li, C.-J. Zhang, X.-B. Zou, and G.-C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Comm. 1, 7 (2010).
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H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011).
[Crossref] [PubMed]

Lipp, Y.O.

B. Dakic, Y.O. Lipp, X.S. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, C. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
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J. G. Rarity, P. R. Tapster, and R. Loudon, “Non-classical interference between independent sources,” J. Opt. B: Quantum Semiclass. Opt. 7, S171 (2005).
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Ma, X.S.

B. Dakic, Y.O. Lipp, X.S. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, C. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
[Crossref]

Mandarino, A.

A. Mandarino, M. Bina, C. Porto, S. Cialdi, S. Olivares, and M. G. A. Paris, “Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems,” Phys. Rev. A 93, 062118 (2016).
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Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044 (1987).
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V. Chille, N. Quinn, C. Peuntinger, C. Croal, L. Mista, C. Marquardt, G. Leuches, and N. Korolkova, “Quantum nature of Gaussian discord: Experimental evidence and role of system-environment correlations,” Phys. Rev. A 91, 050301 (2015).
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L. Mazzola, J. Piilo, and S. Maniscalco, “Sudden transition between classical and quantum decoherence,” Phys. Rev. Lett. 104, 200401 (2010).
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Meda, A.

Mista, L.

V. Chille, N. Quinn, C. Peuntinger, C. Croal, L. Mista, C. Marquardt, G. Leuches, and N. Korolkova, “Quantum nature of Gaussian discord: Experimental evidence and role of system-environment correlations,” Phys. Rev. A 91, 050301 (2015).
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K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: Discord and related measures,” Rev. Mod. Phys. 84, 1655 (2012).
[Crossref]

K. Modi, H. Cable, M. Williamson, and V. Vedral, “Quantum correlations in mixed-state metrology,” Phys. Rev. X 1, 021022 (2011).

Moon, S.

Mor, T.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070 (1999).
[Crossref]

Munro, W. J.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[Crossref]

Niset, J.

J. Niset and N. J. Cerf, “Multipartite nonlocality without entanglement in many dimensions,” Phys. Rev. A 74, 052103 (2006).
[Crossref]

Olivares, S.

A. Mandarino, M. Bina, C. Porto, S. Cialdi, S. Olivares, and M. G. A. Paris, “Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems,” Phys. Rev. A 93, 062118 (2016).
[Crossref]

A. Meda, S. Olivares, I. P. Degiovanni, G. Brida, M. Genovese, and M. G. A. Paris, “Revealing interference by continuous variable discordant states,” Opt. Lett. 38, 3099–3102 (2013).
[Crossref] [PubMed]

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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).
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H. Ollivier and W.H. Zurek, “Quantum discord: A measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
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M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus nonlocal information in quantum-information theory: Formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[Crossref]

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044 (1987).
[Crossref] [PubMed]

Paris, M. G. A.

A. Mandarino, M. Bina, C. Porto, S. Cialdi, S. Olivares, and M. G. A. Paris, “Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems,” Phys. Rev. A 93, 062118 (2016).
[Crossref]

A. Meda, S. Olivares, I. P. Degiovanni, G. Brida, M. Genovese, and M. G. A. Paris, “Revealing interference by continuous variable discordant states,” Opt. Lett. 38, 3099–3102 (2013).
[Crossref] [PubMed]

C. Benedetti, A. P. Shurupov, M. G. A. Paris, G. Brida, and M. Genovese, “Experimental estimation of quantum discord for a polarization qubit and the use of fidelity to assess quantum correlations,” Phys. Rev. A 87, 052136 (2013).
[Crossref]

A. Ferraro and M. G. A. Paris, “Nonclassicality criteria from phase-space representations and information-theoretical constraints are maximally inequivalent,” Phys. Rev. Lett. 108, 260403 (2012).
[Crossref] [PubMed]

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Homodyne estimation of Gaussian quantum discord,” Phys. Rev. Lett. 109, 180402 (2012).
[Crossref] [PubMed]

K. Banaszek, G. M. D’Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (1999).
[Crossref]

Park, B. K.

Paterek, T.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: Discord and related measures,” Rev. Mod. Phys. 84, 1655 (2012).
[Crossref]

B. Dakic, Y.O. Lipp, X.S. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, C. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
[Crossref]

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L. Zhang, A. K. Pati, and J. Wu, “Interference visibility, entanglement, and quantum correlation,” Phys. Rev. A 92, 022316 (2015).
[Crossref]

Peuntinger, C.

V. Chille, N. Quinn, C. Peuntinger, C. Croal, L. Mista, C. Marquardt, G. Leuches, and N. Korolkova, “Quantum nature of Gaussian discord: Experimental evidence and role of system-environment correlations,” Phys. Rev. A 91, 050301 (2015).
[Crossref]

Piilo, J.

L. Mazzola, J. Piilo, and S. Maniscalco, “Sudden transition between classical and quantum decoherence,” Phys. Rev. Lett. 104, 200401 (2010).
[Crossref] [PubMed]

Pirandola, S.

S. Pirandola, “Quantum discord as a resource for quantum cryptography,” Sci. Rep. 4, 6956 (2014).
[Crossref] [PubMed]

Porto, C.

A. Mandarino, M. Bina, C. Porto, S. Cialdi, S. Olivares, and M. G. A. Paris, “Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems,” Phys. Rev. A 93, 062118 (2016).
[Crossref]

Quinn, N.

V. Chille, N. Quinn, C. Peuntinger, C. Croal, L. Mista, C. Marquardt, G. Leuches, and N. Korolkova, “Quantum nature of Gaussian discord: Experimental evidence and role of system-environment correlations,” Phys. Rev. A 91, 050301 (2015).
[Crossref]

Ra, Y.-S.

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011).
[Crossref] [PubMed]

Rahimi-Keshari, S.

S. Hosseini, S. Rahimi-Keshari, J. Y. Haw, S. M. Assad, H. M. Chrzanowski, J. Janousek, T. Symul, T. C. Ralph, and P. K. Lam, “Experimental verification of quantum discord in continuous-variable states,” J. Phys. B: At. Mol. Opt. Phys. 47, 025503 (2014).
[Crossref]

Rains, E.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070 (1999).
[Crossref]

Ralph, T. C.

M. P. Almeida, M. Gu, A. Fedrizzi, M. A. Broome, T. C. Ralph, and A. G. White, “Entanglement-free certification of entangling gates,” Phys. Rev. A 89, 042323 (2014).
[Crossref]

S. Hosseini, S. Rahimi-Keshari, J. Y. Haw, S. M. Assad, H. M. Chrzanowski, J. Janousek, T. Symul, T. C. Ralph, and P. K. Lam, “Experimental verification of quantum discord in continuous-variable states,” J. Phys. B: At. Mol. Opt. Phys. 47, 025503 (2014).
[Crossref]

Rarity, J. G.

J. G. Rarity, P. R. Tapster, and R. Loudon, “Non-classical interference between independent sources,” J. Opt. B: Quantum Semiclass. Opt. 7, S171 (2005).
[Crossref]

Ringbauer, M.

B. Dakic, Y.O. Lipp, X.S. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, C. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
[Crossref]

Sacchi, M. F.

K. Banaszek, G. M. D’Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (1999).
[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]

Sen, A.

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus nonlocal information in quantum-information theory: Formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[Crossref]

Sen, U.

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus nonlocal information in quantum-information theory: Formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[Crossref]

Shabani, A.

A. Shabani and D. A. Lidar, “Vanishing quantum discord is necessary and sufficient for completely positive maps,” Phys. Rev. Lett. 102, 100402 (2009).
[Crossref] [PubMed]

Shaji, A.

A. Datta, A. Shaji, and C. M. Caves, “Quantum discord and the power of one qubit,” Phys. Rev. Lett. 100, 050502 (2008).
[Crossref] [PubMed]

Shih, Y. H.

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett 61, 2921 (1998).
[Crossref]

Shor, P. W.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070 (1999).
[Crossref]

Shurupov, A. P.

C. Benedetti, A. P. Shurupov, M. G. A. Paris, G. Brida, and M. Genovese, “Experimental estimation of quantum discord for a polarization qubit and the use of fidelity to assess quantum correlations,” Phys. Rev. A 87, 052136 (2013).
[Crossref]

Slattery, O.

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Two-photon interference with continuous-wave multi-mode coherent light,” Opt. Express 22, 3611 (2014).
[Crossref] [PubMed]

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

Smolin, J. A.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070 (1999).
[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]

Son, W.

M. S. Kim, W. Son, V. Bužek, and P. L. Knight, “Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement,” Phys. Rev. A 65, 032323 (2002).
[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.

S. Hosseini, S. Rahimi-Keshari, J. Y. Haw, S. M. Assad, H. M. Chrzanowski, J. Janousek, T. Symul, T. C. Ralph, and P. K. Lam, “Experimental verification of quantum discord in continuous-variable states,” J. Phys. B: At. Mol. Opt. Phys. 47, 025503 (2014).
[Crossref]

Synak-Radtke, B.

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus nonlocal information in quantum-information theory: Formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[Crossref]

Tang, X.

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Two-photon interference with continuous-wave multi-mode coherent light,” Opt. Express 22, 3611 (2014).
[Crossref] [PubMed]

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

Tapster, P. R.

J. G. Rarity, P. R. Tapster, and R. Loudon, “Non-classical interference between independent sources,” J. Opt. B: Quantum Semiclass. Opt. 7, S171 (2005).
[Crossref]

Terno, D. R.

A. Brodutch and D. R. Terno, “Quantum discord, local operations, and Maxwell’s demons,” Phys. Rev. A 81, 062103 (2010).
[Crossref]

Tualle-Brouri, R.

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Homodyne estimation of Gaussian quantum discord,” Phys. Rev. Lett. 109, 180402 (2012).
[Crossref] [PubMed]

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.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: Discord and related measures,” Rev. Mod. Phys. 84, 1655 (2012).
[Crossref]

B. Dakic, Y.O. Lipp, X.S. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, C. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
[Crossref]

K. Modi, H. Cable, M. Williamson, and V. Vedral, “Quantum correlations in mixed-state metrology,” Phys. Rev. X 1, 021022 (2011).

L. Henderson and V. Vedral, “Classical, quantum and total correlations,” J. Phys. A: Math. Gen. 34, 6899 (2001).
[Crossref]

Walther, P.

B. Dakic, Y.O. Lipp, X.S. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, C. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
[Crossref]

Wang, X.-B.

X.-B. Wang, “Theorem for the beam-splitter entangler,” Phys. Rev. A 66, 024303 (2002).
[Crossref]

White, A. G.

M. P. Almeida, M. Gu, A. Fedrizzi, M. A. Broome, T. C. Ralph, and A. G. White, “Entanglement-free certification of entangling gates,” Phys. Rev. A 89, 042323 (2014).
[Crossref]

B. P. Lanyon, M. Barbieri, M. P. Almeida, and A. G. White, “Experimental quantum computing without entanglement,” Phys. Rev. Lett. 101, 200501 (2008).
[Crossref] [PubMed]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[Crossref]

Williamson, M.

K. Modi, H. Cable, M. Williamson, and V. Vedral, “Quantum correlations in mixed-state metrology,” Phys. Rev. X 1, 021022 (2011).

Wootters, W. K.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070 (1999).
[Crossref]

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245 (1998).
[Crossref]

Wu, J.

L. Zhang, A. K. Pati, and J. Wu, “Interference visibility, entanglement, and quantum correlation,” Phys. Rev. A 92, 022316 (2015).
[Crossref]

Xu, J.-S.

J.-S. Xu, X.-Y. Xu, C.-F. Li, C.-J. Zhang, X.-B. Zou, and G.-C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Comm. 1, 7 (2010).
[Crossref]

Xu, X.-Y.

J.-S. Xu, X.-Y. Xu, C.-F. Li, C.-J. Zhang, X.-B. Zou, and G.-C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Comm. 1, 7 (2010).
[Crossref]

Yune, J.

Zaraket, H.

S. Hamieh, R. Kobes, and H. Zaraket, “Positive-operator-valued measure optimization of classical correlations,” Phys. Rev. A 70, 052325 (2004).
[Crossref]

Zeilinger, A.

B. Dakic, Y.O. Lipp, X.S. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, C. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
[Crossref]

Zhang, C.-J.

J.-S. Xu, X.-Y. Xu, C.-F. Li, C.-J. Zhang, X.-B. Zou, and G.-C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Comm. 1, 7 (2010).
[Crossref]

Zhang, L.

L. Zhang, A. K. Pati, and J. Wu, “Interference visibility, entanglement, and quantum correlation,” Phys. Rev. A 92, 022316 (2015).
[Crossref]

Zou, X.-B.

J.-S. Xu, X.-Y. Xu, C.-F. Li, C.-J. Zhang, X.-B. Zou, and G.-C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Comm. 1, 7 (2010).
[Crossref]

Zurek, W. H.

W. H. Zurek, “Quantum discord and Maxwell’s demons,” Phys. Rev. A 67, 012320 (2003).
[Crossref]

Zurek, W.H.

H. Ollivier and W.H. Zurek, “Quantum discord: A measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
[Crossref]

Appl. Opt. (1)

J. Opt. B: Quantum Semiclass. Opt. (1)

J. G. Rarity, P. R. Tapster, and R. Loudon, “Non-classical interference between independent sources,” J. Opt. B: Quantum Semiclass. Opt. 7, S171 (2005).
[Crossref]

J. Phys. A: Math. Gen. (1)

L. Henderson and V. Vedral, “Classical, quantum and total correlations,” J. Phys. A: Math. Gen. 34, 6899 (2001).
[Crossref]

J. Phys. B: At. Mol. Opt. Phys. (1)

S. Hosseini, S. Rahimi-Keshari, J. Y. Haw, S. M. Assad, H. M. Chrzanowski, J. Janousek, T. Symul, T. C. Ralph, and P. K. Lam, “Experimental verification of quantum discord in continuous-variable states,” J. Phys. B: At. Mol. Opt. Phys. 47, 025503 (2014).
[Crossref]

Nat. Comm. (1)

J.-S. Xu, X.-Y. Xu, C.-F. Li, C.-J. Zhang, X.-B. Zou, and G.-C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Comm. 1, 7 (2010).
[Crossref]

Nat. Phys. (2)

Y.-S. Kim, J-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nat. Phys. 8, 117 (2012).
[Crossref]

B. Dakic, Y.O. Lipp, X.S. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, C. Brukner, and P. Walther, “Quantum discord as resource for remote state preparation,” Nat. Phys. 8, 666–670 (2012).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (17)

L. Zhang, A. K. Pati, and J. Wu, “Interference visibility, entanglement, and quantum correlation,” Phys. Rev. A 92, 022316 (2015).
[Crossref]

A. Ferraro, L. Aolita, D. Cavalcanti, F. M. Cucchietti, and A. Acín, “Almost all quantum states have nonclassical correlations,” Phys. Rev. A 81, 052318 (2010).
[Crossref]

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070 (1999).
[Crossref]

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus nonlocal information in quantum-information theory: Formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[Crossref]

J. Niset and N. J. Cerf, “Multipartite nonlocality without entanglement in many dimensions,” Phys. Rev. A 74, 052103 (2006).
[Crossref]

V. Chille, N. Quinn, C. Peuntinger, C. Croal, L. Mista, C. Marquardt, G. Leuches, and N. Korolkova, “Quantum nature of Gaussian discord: Experimental evidence and role of system-environment correlations,” Phys. Rev. A 91, 050301 (2015).
[Crossref]

W. H. Zurek, “Quantum discord and Maxwell’s demons,” Phys. Rev. A 67, 012320 (2003).
[Crossref]

A. Brodutch and D. R. Terno, “Quantum discord, local operations, and Maxwell’s demons,” Phys. Rev. A 81, 062103 (2010).
[Crossref]

K. Banaszek, G. M. D’Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (1999).
[Crossref]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[Crossref]

C. Benedetti, A. P. Shurupov, M. G. A. Paris, G. Brida, and M. Genovese, “Experimental estimation of quantum discord for a polarization qubit and the use of fidelity to assess quantum correlations,” Phys. Rev. A 87, 052136 (2013).
[Crossref]

A. Mandarino, M. Bina, C. Porto, S. Cialdi, S. Olivares, and M. G. A. Paris, “Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems,” Phys. Rev. A 93, 062118 (2016).
[Crossref]

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

M. S. Kim, W. Son, V. Bužek, and P. L. Knight, “Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement,” Phys. Rev. A 65, 032323 (2002).
[Crossref]

X.-B. Wang, “Theorem for the beam-splitter entangler,” Phys. Rev. A 66, 024303 (2002).
[Crossref]

M. P. Almeida, M. Gu, A. Fedrizzi, M. A. Broome, T. C. Ralph, and A. G. White, “Entanglement-free certification of entangling gates,” Phys. Rev. A 89, 042323 (2014).
[Crossref]

S. Hamieh, R. Kobes, and H. Zaraket, “Positive-operator-valued measure optimization of classical correlations,” Phys. Rev. A 70, 052325 (2004).
[Crossref]

Phys. Rev. Lett (1)

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett 61, 2921 (1998).
[Crossref]

Phys. Rev. Lett. (11)

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, and Y.-H Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011).
[Crossref] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044 (1987).
[Crossref] [PubMed]

A. Ferraro and M. G. A. Paris, “Nonclassicality criteria from phase-space representations and information-theoretical constraints are maximally inequivalent,” Phys. Rev. Lett. 108, 260403 (2012).
[Crossref] [PubMed]

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]

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245 (1998).
[Crossref]

A. Shabani and D. A. Lidar, “Vanishing quantum discord is necessary and sufficient for completely positive maps,” Phys. Rev. Lett. 102, 100402 (2009).
[Crossref] [PubMed]

L. Mazzola, J. Piilo, and S. Maniscalco, “Sudden transition between classical and quantum decoherence,” Phys. Rev. Lett. 104, 200401 (2010).
[Crossref] [PubMed]

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Homodyne estimation of Gaussian quantum discord,” Phys. Rev. Lett. 109, 180402 (2012).
[Crossref] [PubMed]

A. Datta, A. Shaji, and C. M. Caves, “Quantum discord and the power of one qubit,” Phys. Rev. Lett. 100, 050502 (2008).
[Crossref] [PubMed]

B. P. Lanyon, M. Barbieri, M. P. Almeida, and A. G. White, “Experimental quantum computing without entanglement,” Phys. Rev. Lett. 101, 200501 (2008).
[Crossref] [PubMed]

H. Ollivier and W.H. Zurek, “Quantum discord: A measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
[Crossref]

Phys. Rev. X (1)

K. Modi, H. Cable, M. Williamson, and V. Vedral, “Quantum correlations in mixed-state metrology,” Phys. Rev. X 1, 021022 (2011).

Rev. Mod. Phys. (2)

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: Discord and related measures,” Rev. Mod. Phys. 84, 1655 (2012).
[Crossref]

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865 (2009).
[Crossref]

Sci. Rep. (1)

S. Pirandola, “Quantum discord as a resource for quantum cryptography,” Sci. Rep. 4, 6956 (2014).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 Experimental setup where the phase of the two input pulses are mutually (a) coherent and (b) incoherent. fs-laser : femtosecond laser, filter set : filter set of neutral density filters and an interference filter, BS : 50:50 beamsplitter, AOM : acousto-optic modulator, FC : fiber coupler, PC : polarization controller, FBS : fiber beamsplitter, C : collimation lens, Q : quarter-wave plate, H : half-wave plate, P : polarizer, SPD : single photon detector, CCU : coincidence counting unit.
Fig. 2
Fig. 2 Two-qubit density matrices where the phase of the pulses incident on the two input modes of a BS are mutually (a) coherent or (b) incoherent. ρ c o h ( ρ c o h exp ) is the theoretical (experimental) density matrix of the coherent case. ρ i n c o h ( ρ c o h exp ) is the theoretical (experimental) density matrix of the incoherent case. Re[·] and Im[·] denote the real and imaginary parts of the density matrix, respectively.
Fig. 3
Fig. 3 Classical Hong-Ou-Mandel dip. The means and standard deviations of the coincidence count rate data are represented with blue circles and error bars, respectively. The red solid line denotes the Gaussian fitting for the data. The visibility of the dip, V, is calculated from the fitted Gaussian function.
Fig. 4
Fig. 4 Purity (red and right vertical axis) and discord (blue and left vertical axis) versus the optical path length difference for mutually incoherent case. The circles and error bars denote the experimental average values and standard deviations, respectively. The solid lines are the Gaussian fittings for the data.
Fig. 5
Fig. 5 The proportion of the erroneous coincidence detections due to multi-photon states.

Tables (1)

Tables Icon

Table 1 Characteristics of the theoretical and experimental two-qubit density matrices. ρmixed is the two-qubit state when the optical path length difference between two mutually incoherent optical pulses are larger than the coherence length of the optical pulses.

Equations (23)

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

I ( A : B ) = H ( A ) + H ( B ) H ( A , B ) ,
J ( A : B ) = H ( A ) H ( A | B ) .
D ( ρ A B ) { Π j B } = I ( ρ A B ) J ( ρ A B ) { Π j B }
D ( ρ A B ) = I ( ρ A B ) max { Π j B } J ( ρ A B ) { Π j B } .
ρ c o h ( ϕ ) = 1 4 ( 1 i e i ϕ i e i ϕ i e 2 i ϕ i e i ϕ 1 1 i e i ϕ i e i ϕ 1 1 i e i ϕ i e 2 i ϕ i e i ϕ i e i ϕ 1 )
ρ i n c o h = 1 4 ( 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 )
ρ c o h | c ( ϕ ) = 1 2 ( 1 i e i ϕ i e i ϕ 1 ) ,
ρ c o h | d ( ϕ ) = 1 2 ( 1 i e i ϕ i e i ϕ 1 ) ,
ρ i n c o h | c = ρ i n c o h | d = 1 2 ( 1 0 0 1 ) ,
( a b ) 1 2 ( 1 i i 1 ) ( c d )
| α = e | α | 2 / 2 m = 0 α m m ! ( a H ) m | 0
| β = e | β | 2 / 2 n = 0 β n n ! ( e i ϕ b V ) n | 0
| ψ c o h i n = e μ m , n = 0 μ ( m + n ) / 2 m ! n ! ( a H ) m ( e i ϕ b V ) n | 0 | 0 .
| ψ c o h o u t = e μ m , n = 0 ( μ / 2 ) ( m + n ) / 2 m ! n ! ( c H + i d H ) m ( e i ϕ ( i c V + d V ) ) n | 0 | 0 .
| ψ c o h = 1 2 ( i c H d H + e i ϕ c H d V e i ϕ c V d H + i e i 2 ϕ c V d V ) | 0 | 0 .
| ψ ( 1 , 1 ) = 1 2 ( i c H c V + c H d V c V d H + i d H d V ) | 0 | 0 .
ρ i n c o h ( 1 , 1 ) = 1 2 ( 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 ) ,
| ψ ( 2 , 0 ) = 1 2 2 ( ( c H ) 2 + 2 i c H d H ( d H ) 2 ) | 0 | 0 .
ρ i n c o h ( 2 , 0 ) = ( 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ) .
| ψ ( 0 , 2 ) = 1 2 2 ( ( c V ) 2 + 2 i c V d V + ( d V ) 2 ) | 0 | 0 .
ρ i n c o h ( 0 , 2 ) = ( 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ) .
ρ i n c o h = p ( 1 , 1 ) ρ i n c o h ( 1 , 1 ) + p ( 2 , 0 ) ρ i n c o h ( 2 , 0 ) + p ( 0 , 2 ) ρ i n c o h ( 0 , 2 ) Tr [ p ( 1 , 1 ) ρ i n c o h ( 1 , 1 ) + p ( 2 , 0 ) ρ i n c o h ( 2 , 0 ) + p ( 0 , 2 ) ρ i n c o h ( 0 , 2 ) ]
E ( μ ) = i + j 3 p ( μ , i , j ) i + j 2 p ( μ , i , j )

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