Almost all quantum states have nonclassical correlations

doi:https://doi.org/10.1103/PHYSREVA.81.052318

Title: Almost all quantum states have nonclassical correlations

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Abstract

Quantum discord quantifies nonclassical correlations in a quantum system including those not captured by entanglement. Thus, only states with zero discord exhibit strictly classical correlations. We prove that these states are negligible in the whole Hilbert space: typically a state picked out at random has positive discord and, given a state with zero discord, a generic arbitrarily small perturbation drives it to a positive-discord state. These results hold for any Hilbert-space dimension and have direct implications for quantum computation and for the foundations of the theory of open systems. In addition, we provide a simple necessary criterion for zero quantum discord. Finally, we show that, for almost all positive-discord states, an arbitrary Markovian evolution cannot lead to a sudden, permanent vanishing of discord.

Authors:

Ferraro, A; Aolita, L; Cavalcanti, D; Cucchietti, F M ^[1]; Acin, A ^[1]

Institut de Ciencies Fotoniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona) (Spain)

Publication Date:: 2010-05-15

OSTI Identifier:: 21408794

Resource Type:: Journal Article

Journal Name:: Physical Review. A

Additional Journal Information:: Journal Volume: 81; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.81.052318; (c) 2010 The American Physical Society; Journal ID: ISSN 1050-2947

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATIONS; HILBERT SPACE; MARKOV PROCESS; MATHEMATICAL EVOLUTION; PERTURBATION THEORY; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; RANDOMNESS; BANACH SPACE; COMPUTERS; EVOLUTION; MATHEMATICAL SPACE; SPACE; STOCHASTIC PROCESSES

Citation Formats


                    Ferraro, A, Aolita, L, Cavalcanti, D, Cucchietti, F M, Acin, A, and Institucio Catalana de Recerca i Estudis Avancats, Lluis Companys 23, E-08010 Barcelona. Almost all quantum states have nonclassical correlations.  United States: N. p., 2010. 
        Web.  doi:10.1103/PHYSREVA.81.052318.

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                    Ferraro, A, Aolita, L, Cavalcanti, D, Cucchietti, F M, Acin, A, & Institucio Catalana de Recerca i Estudis Avancats, Lluis Companys 23, E-08010 Barcelona. Almost all quantum states have nonclassical correlations.  United States.  https://doi.org/10.1103/PHYSREVA.81.052318

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                    Ferraro, A, Aolita, L, Cavalcanti, D, Cucchietti, F M, Acin, A, and Institucio Catalana de Recerca i Estudis Avancats, Lluis Companys 23, E-08010 Barcelona. Sat .  
        "Almost all quantum states have nonclassical correlations".  United States.  https://doi.org/10.1103/PHYSREVA.81.052318.

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@article{osti_21408794,

  title        = {Almost all quantum states have nonclassical correlations},

  author       = {Ferraro, A and Aolita, L and Cavalcanti, D and Cucchietti, F M and Acin, A and Institucio Catalana de Recerca i Estudis Avancats, Lluis Companys 23, E-08010 Barcelona},

  abstractNote = {Quantum discord quantifies nonclassical correlations in a quantum system including those not captured by entanglement. Thus, only states with zero discord exhibit strictly classical correlations. We prove that these states are negligible in the whole Hilbert space: typically a state picked out at random has positive discord and, given a state with zero discord, a generic arbitrarily small perturbation drives it to a positive-discord state. These results hold for any Hilbert-space dimension and have direct implications for quantum computation and for the foundations of the theory of open systems. In addition, we provide a simple necessary criterion for zero quantum discord. Finally, we show that, for almost all positive-discord states, an arbitrary Markovian evolution cannot lead to a sudden, permanent vanishing of discord.},

  doi          = {10.1103/PHYSREVA.81.052318},

  url          = {https://www.osti.gov/biblio/21408794},
  journal      = {Physical Review. A},

  issn         = {1050-2947},

  number       = 5,

  volume       = 81,

  place        = {United States},

  year         = {2010},

  month        = {5}

}

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https://doi.org/10.1103/PHYSREVA.81.052318

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