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. © 2010 The American Physical Society.
Almost all quantum states have nonclassical correlations / A. Ferraro, L. Aolita, D. Cavalcanti, F.M. Cucchietti, A. Acin. - In: PHYSICAL REVIEW A. - ISSN 1050-2947. - 81:5(2010 May), pp. 052318.1-052318.6. [10.1103/PhysRevA.81.052318]
Almost all quantum states have nonclassical correlations
A. Ferraro
Primo
;
2010
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. © 2010 The American Physical Society.File | Dimensione | Formato | |
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