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Erschienen in: Quantum Information Processing 5/2016

01.05.2016

Revealing quantum correlation by negativity of the Wigner function

verfasst von: Razieh Taghiabadi, Seyed Javad Akhtarshenas, Mohsen Sarbishaei

Erschienen in: Quantum Information Processing | Ausgabe 5/2016

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Abstract

We analyze two two-mode continuous variable separable states with the same marginal states. We adopt the definition of classicality in the form of well-defined positive Wigner function describing the state and find that although the states possess positive local Wigner functions, they exhibit negative Wigner functions for the global states. Using the negativity of Wigner function as an indicator of nonclassicality, we show that despite these states possess different negativities of the Wigner function, they do not reveal this difference as phase space nonclassicalities such as negativity of the Mandel Q parameter or quadrature squeezing. We then concentrate on quantum correlation of these states and show that quantum discord and local quantum uncertainty, as two well-defined measures of quantum correlation, manifest the difference between negativity of the Wigner functions. The non-Gaussianity of these states is also examined and show that the difference in behavior of their non-Gaussianity is the same as the difference between negativity of their Wigner functions. We also investigate the influence of correlation rank criterion and find that when the states can be produced locally from classical states, the Wigner functions cannot reveal their quantum correlations.

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Literatur
1.
Zurück zum Zitat Cahill, K.E., Glauber, R.J.: Density operators and quasiprobability distributions. Phys. Rev. 177, 1882–1902 (1969)ADSCrossRef Cahill, K.E., Glauber, R.J.: Density operators and quasiprobability distributions. Phys. Rev. 177, 1882–1902 (1969)ADSCrossRef
2.
Zurück zum Zitat Husimi, K.: Some formal properties of the density matrix. Proc. Phys. Math. Soc. Jpn. 22, 264–314 (1940)MATH Husimi, K.: Some formal properties of the density matrix. Proc. Phys. Math. Soc. Jpn. 22, 264–314 (1940)MATH
4.
Zurück zum Zitat Sudarshan, E.C.G.: Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams. Phys. Rev. Lett. 10, 277–279 (1963)ADSMathSciNetCrossRefMATH Sudarshan, E.C.G.: Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams. Phys. Rev. Lett. 10, 277–279 (1963)ADSMathSciNetCrossRefMATH
5.
Zurück zum Zitat Wigner, E.P.: On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749–759 (1932)ADSCrossRefMATH Wigner, E.P.: On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749–759 (1932)ADSCrossRefMATH
6.
8.
Zurück zum Zitat Soto, F., Claverie, P.: When is the Wigner function of multidimensional systems nonnegative? J. Math. Phys. 24, 97–100 (1983)ADSMathSciNetCrossRef Soto, F., Claverie, P.: When is the Wigner function of multidimensional systems nonnegative? J. Math. Phys. 24, 97–100 (1983)ADSMathSciNetCrossRef
10.
Zurück zum Zitat Mandilara, A., Karpov, E., Cerf, N.J.: Extending Hudson’s theorem to mixed quantum states. Phys. Rev. A 79, 062302 (2009)ADSMathSciNetCrossRef Mandilara, A., Karpov, E., Cerf, N.J.: Extending Hudson’s theorem to mixed quantum states. Phys. Rev. A 79, 062302 (2009)ADSMathSciNetCrossRef
11.
Zurück zum Zitat Genoni, M.G., Palma, M.L., Tufarelli, T., Olivares, S., Kim, M.S., Paris, M.G.A.: Detecting quantum non-Gaussianity via the Wigner function. Phys. Rev. A 87, 062104 (2013)ADSCrossRef Genoni, M.G., Palma, M.L., Tufarelli, T., Olivares, S., Kim, M.S., Paris, M.G.A.: Detecting quantum non-Gaussianity via the Wigner function. Phys. Rev. A 87, 062104 (2013)ADSCrossRef
12.
Zurück zum Zitat Hughes, C., Genoni, M.G., Tufarelli, T., Paris, M.G.A., Kim, M.S.: Quantum non-Gaussianity witnesses in phase space. Phys. Rev. A 90, 013810 (2014)ADSCrossRef Hughes, C., Genoni, M.G., Tufarelli, T., Paris, M.G.A., Kim, M.S.: Quantum non-Gaussianity witnesses in phase space. Phys. Rev. A 90, 013810 (2014)ADSCrossRef
13.
Zurück zum Zitat Mari, A., Eisert, J.: Positive Wigner functions render classical simulation of quantum computation efficient. Phys. Rev. Lett. 109, 230503 (2012)ADSCrossRef Mari, A., Eisert, J.: Positive Wigner functions render classical simulation of quantum computation efficient. Phys. Rev. Lett. 109, 230503 (2012)ADSCrossRef
14.
Zurück zum Zitat Veitch, V., Wiebe, N., Ferrie, C., Emerson, J.: Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation. New J. Phys. 15, 013037 (2013)ADSCrossRef Veitch, V., Wiebe, N., Ferrie, C., Emerson, J.: Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation. New J. Phys. 15, 013037 (2013)ADSCrossRef
15.
Zurück zum Zitat Kenfack, A., Zyczkowski, K.: Negativity of the Wigner function as an indicator of non-classicality. J. Opt. B 6, 396–404 (2004)ADSMathSciNetCrossRef Kenfack, A., Zyczkowski, K.: Negativity of the Wigner function as an indicator of non-classicality. J. Opt. B 6, 396–404 (2004)ADSMathSciNetCrossRef
16.
Zurück zum Zitat Mari, A., Kieling, K., Nielsen, B.M., Polzik, E.S., Eisert, J.: Directly estimating nonclassicality. Phys. Rev. Lett. 106, 010403 (2011)ADSCrossRef Mari, A., Kieling, K., Nielsen, B.M., Polzik, E.S., Eisert, J.: Directly estimating nonclassicality. Phys. Rev. Lett. 106, 010403 (2011)ADSCrossRef
17.
Zurück zum Zitat Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)ADSCrossRefMATH Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)ADSCrossRefMATH
18.
Zurück zum Zitat Schrödinger, E.: Die gegenwartige situation in der quanenmechanik. Naturwissenschaften 23, 807–812 (1935)ADSCrossRefMATH Schrödinger, E.: Die gegenwartige situation in der quanenmechanik. Naturwissenschaften 23, 807–812 (1935)ADSCrossRefMATH
19.
Zurück zum Zitat Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRefMATH Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRefMATH
21.
Zurück zum Zitat Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277–4281 (1989)ADSCrossRef Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277–4281 (1989)ADSCrossRef
22.
Zurück zum Zitat Marek, P., Kim, M.S., Lee, J.: Nonclassicality in phase space and nonclassical correlation. Phys. Rev. A 79, 052315 (2009)ADSMathSciNetCrossRef Marek, P., Kim, M.S., Lee, J.: Nonclassicality in phase space and nonclassical correlation. Phys. Rev. A 79, 052315 (2009)ADSMathSciNetCrossRef
23.
Zurück zum Zitat Knill, E., Laflamme, R.: Power of one bit of quantum information. Phys. Rev. Lett. 81, 5672–5675 (1998)ADSCrossRef Knill, E., Laflamme, R.: Power of one bit of quantum information. Phys. Rev. Lett. 81, 5672–5675 (1998)ADSCrossRef
24.
Zurück zum Zitat Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008)ADSCrossRef Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008)ADSCrossRef
25.
Zurück zum Zitat Ferraro, A., Paris, M.G.A.: Nonclassicality criteria from phase-space representations and information-theoretical constraints are maximally inequivalent. Phys. Rev. Lett. 108, 260403 (2012)ADSCrossRef Ferraro, A., Paris, M.G.A.: Nonclassicality criteria from phase-space representations and information-theoretical constraints are maximally inequivalent. Phys. Rev. Lett. 108, 260403 (2012)ADSCrossRef
26.
Zurück zum Zitat Dakic, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)ADSCrossRefMATH Dakic, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)ADSCrossRefMATH
27.
Zurück zum Zitat Mani, A., Karimipour, V., Memarzadeh, L.: Comparison of parallel and antiparallel two-qubit mixed states. Phys. Rev. A 91, 012304 (2015)ADSMathSciNetCrossRef Mani, A., Karimipour, V., Memarzadeh, L.: Comparison of parallel and antiparallel two-qubit mixed states. Phys. Rev. A 91, 012304 (2015)ADSMathSciNetCrossRef
28.
Zurück zum Zitat Girolami, D., Tufarelli, T., Adesso, G.: Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. Lett. 110, 240402 (2013)ADSCrossRef Girolami, D., Tufarelli, T., Adesso, G.: Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. Lett. 110, 240402 (2013)ADSCrossRef
29.
Zurück zum Zitat Klauder, J.R.: The action option and a Feynman quantization of spinor fields in terms of ordinary c-numbers. Ann. Phys. (N.Y.) 11, 123–168 (1960)ADSMathSciNetCrossRefMATH Klauder, J.R.: The action option and a Feynman quantization of spinor fields in terms of ordinary c-numbers. Ann. Phys. (N.Y.) 11, 123–168 (1960)ADSMathSciNetCrossRefMATH
30.
Zurück zum Zitat Dodonov, V., Malkin, I.A., Manko, V.I.: Even and odd coherent states and excitations of a singular oscillator. Physica 72, 597–615 (1974)ADSMathSciNetCrossRef Dodonov, V., Malkin, I.A., Manko, V.I.: Even and odd coherent states and excitations of a singular oscillator. Physica 72, 597–615 (1974)ADSMathSciNetCrossRef
31.
Zurück zum Zitat Ansari, A.N., Manko, V.I.: Photon statistics of multimode even and odd coherent light. Phys. Rev. A 50, 1942–1945 (1994)ADSCrossRef Ansari, A.N., Manko, V.I.: Photon statistics of multimode even and odd coherent light. Phys. Rev. A 50, 1942–1945 (1994)ADSCrossRef
32.
Zurück zum Zitat Genoni, M.G., Invernizzi, C., Paris, M.G.A.: Enhancement of parameter estimation by Kerr interaction. Phys. Rev. A 80, 033842 (2009)ADSCrossRef Genoni, M.G., Invernizzi, C., Paris, M.G.A.: Enhancement of parameter estimation by Kerr interaction. Phys. Rev. A 80, 033842 (2009)ADSCrossRef
33.
Zurück zum Zitat Adesso, G., DellAnno, F., De Siena, S., Illuminati, F., Souza, L.A.M.: Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states. Phys. Rev. A 79, 040305(R) (2009)ADSCrossRef Adesso, G., DellAnno, F., De Siena, S., Illuminati, F., Souza, L.A.M.: Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states. Phys. Rev. A 79, 040305(R) (2009)ADSCrossRef
34.
Zurück zum Zitat Lütkenhaus, N., Barnett, S.M.: Nonclassical effects in phase space. Phys. Rev. A 51, 3340–3342 (1995)ADSCrossRef Lütkenhaus, N., Barnett, S.M.: Nonclassical effects in phase space. Phys. Rev. A 51, 3340–3342 (1995)ADSCrossRef
35.
Zurück zum Zitat Genoni, M.G., Paris, M.G.A., Banaszek, K.: Measure of the non-Gaussian character of a quantum state. Phys. Rev. A 76, 042327 (2007)ADSCrossRef Genoni, M.G., Paris, M.G.A., Banaszek, K.: Measure of the non-Gaussian character of a quantum state. Phys. Rev. A 76, 042327 (2007)ADSCrossRef
36.
Zurück zum Zitat Genoni, M.G., Paris, M.G.A., Banaszek, K.: Quantifying the non-Gaussian character of a quantum state by quantum relative entropy. Phys. Rev. A 78, 060303 (2008)ADSMathSciNetCrossRef Genoni, M.G., Paris, M.G.A., Banaszek, K.: Quantifying the non-Gaussian character of a quantum state by quantum relative entropy. Phys. Rev. A 78, 060303 (2008)ADSMathSciNetCrossRef
37.
Zurück zum Zitat Ghiu, I., Marian, P., Marian, T.A.: Measures of non-Gaussianity for one-mode field states. Phys. Scr. 153, 014028 (2013)CrossRef Ghiu, I., Marian, P., Marian, T.A.: Measures of non-Gaussianity for one-mode field states. Phys. Scr. 153, 014028 (2013)CrossRef
38.
Zurück zum Zitat Genoni, G., Paris, G.A.: Quantifying non-Gaussianity for quantum information. Phys. Rev. A 82, 052341 (2010)ADSCrossRef Genoni, G., Paris, G.A.: Quantifying non-Gaussianity for quantum information. Phys. Rev. A 82, 052341 (2010)ADSCrossRef
39.
Zurück zum Zitat Bukhari, S.H., Naeem Khan, S., Ahmad, M.A.: Two-mode superposition coherent states: entanglement and nonclassicality. Acta Phys. Pol. B 42, 2077–2086 (2011)MathSciNetCrossRef Bukhari, S.H., Naeem Khan, S., Ahmad, M.A.: Two-mode superposition coherent states: entanglement and nonclassicality. Acta Phys. Pol. B 42, 2077–2086 (2011)MathSciNetCrossRef
40.
Zurück zum Zitat Hanbury Brown, R., Twiss, R.Q.: A test of a new type of stellar interferometer on Sirius. Nature 178, 1046–1048 (1956)ADSCrossRef Hanbury Brown, R., Twiss, R.Q.: A test of a new type of stellar interferometer on Sirius. Nature 178, 1046–1048 (1956)ADSCrossRef
41.
Zurück zum Zitat Kimble, H.J., Dagenais, M., Mandel, L.: Photon antibunching in resonance fluorescence. Phys. Rev. Lett. 39, 691–695 (1977)ADSCrossRef Kimble, H.J., Dagenais, M., Mandel, L.: Photon antibunching in resonance fluorescence. Phys. Rev. Lett. 39, 691–695 (1977)ADSCrossRef
42.
Zurück zum Zitat Mandel, L.: Sub-Poissonian photon statistics in resonance fluorescence. Opt. Lett. 4, 205–207 (1979)ADSCrossRef Mandel, L.: Sub-Poissonian photon statistics in resonance fluorescence. Opt. Lett. 4, 205–207 (1979)ADSCrossRef
43.
45.
Zurück zum Zitat Chen, Q., Zhang, C., Yu, S., Yi, X.X., Oh, C.H.: Quantum discord of two-qubit X states. Phys. A 84, 042313 (2011)ADSMathSciNet Chen, Q., Zhang, C., Yu, S., Yi, X.X., Oh, C.H.: Quantum discord of two-qubit X states. Phys. A 84, 042313 (2011)ADSMathSciNet
46.
Zurück zum Zitat Akhtarshenas, S.J., Mohammadi, H., Mousavi, F.S., Nassajpour, V.: Progress on quantum discord of two-qubit states: optimization and upper bound. Int. J. Theor. Phys. 54, 72–84 (2015)CrossRefMATH Akhtarshenas, S.J., Mohammadi, H., Mousavi, F.S., Nassajpour, V.: Progress on quantum discord of two-qubit states: optimization and upper bound. Int. J. Theor. Phys. 54, 72–84 (2015)CrossRefMATH
48.
Zurück zum Zitat Gessner, M., Laine, E.M., Breuer, H.P., Piilo, J.: Correlations in quantum states and the local creation of quantum discord. Phys. Rev. A 85, 052122 (2012)ADSCrossRef Gessner, M., Laine, E.M., Breuer, H.P., Piilo, J.: Correlations in quantum states and the local creation of quantum discord. Phys. Rev. A 85, 052122 (2012)ADSCrossRef
49.
Zurück zum Zitat Hong, C.K., Mandel, L.: Higher-order squeezing of a quantum field. Phys. Rev. Lett. 54, 323–325 (1985)ADSCrossRef Hong, C.K., Mandel, L.: Higher-order squeezing of a quantum field. Phys. Rev. Lett. 54, 323–325 (1985)ADSCrossRef
50.
Zurück zum Zitat Zou, X.T., Mandel, L.: Photon-antibunching and sub-Poissonian photon statistics. Phys. Rev. A 41, 475–476 (1990)ADSCrossRef Zou, X.T., Mandel, L.: Photon-antibunching and sub-Poissonian photon statistics. Phys. Rev. A 41, 475–476 (1990)ADSCrossRef
Metadaten
Titel
Revealing quantum correlation by negativity of the Wigner function
verfasst von
Razieh Taghiabadi
Seyed Javad Akhtarshenas
Mohsen Sarbishaei
Publikationsdatum
01.05.2016
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 5/2016
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-016-1255-6

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