Almost all quantum states have non-classical correlations

TL;DR

This paper demonstrates that almost all quantum states possess non-classical correlations, with zero-discord states being negligible and easily perturbed into positive-discord states, impacting quantum computation and open systems theory.

Contribution

It proves the rarity of zero-discord states in the Hilbert space and analyzes their stability under perturbations and evolution.

Findings

Zero-discord states are negligible in the Hilbert space.

Small perturbations typically induce positive discord.

Most positive-discord states cannot have discord permanently vanish under Markovian evolution.

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.