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arXiv · 0908.3157

Almost all quantum states have non-classical correlations

A. Ferraro·L. Aolita·D. Cavalcanti·F. M. Cucchietti·A. Acin
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Abstract

Quantum discord quantifies non-classical 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 on quantum computation and on 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.

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A. Ferraro, L. Aolita, D. Cavalcanti, F. M. Cucchietti, A. Acin. 2010-03-22. Almost all quantum states have non-classical correlations. https://doi.org/10.1103/physreva.81.052318

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