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Title: Almost all quantum states have nonclassical correlations

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:
; ; ;  [1];  [1]
  1. Institut de Ciencies Fotoniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona) (Spain)
Publication Date:
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.
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
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.
@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}
}