### 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.

Original language | English |
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Article number | 052318 |

Number of pages | 6 |

Journal | Physical Review A (Atomic, Molecular, and Optical Physics) |

Volume | 81 |

Issue number | 5 |

DOIs | |

Publication status | Published - 17 May 2010 |

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## Cite this

Ferraro, A., Aolita, L., Cavalcanti, D., Cucchietti, F. M., & Acín, A. (2010). Almost all quantum states have nonclassical correlations.

*Physical Review A (Atomic, Molecular, and Optical Physics)*,*81*(5), [052318]. https://doi.org/10.1103/PhysRevA.81.052318