TY - JOUR

T1 - Almost all quantum states have nonclassical correlations

AU - Ferraro, A.

AU - Aolita, L.

AU - Cavalcanti, D.

AU - Cucchietti, F.M.

AU - Acín, A.

PY - 2010/5/17

Y1 - 2010/5/17

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevA.81.052318

DO - 10.1103/PhysRevA.81.052318

M3 - Article

AN - SCOPUS:77953152871

VL - 81

JO - Physical Review A (Atomic, Molecular, and Optical Physics)

JF - Physical Review A (Atomic, Molecular, and Optical Physics)

SN - 1050-2947

IS - 5

M1 - 052318

ER -