Upper Bounds on the Distillable Randomness of Bipartite Quantum States

TL;DR

This paper introduces new upper bounds on the distillable randomness of bipartite quantum states, making it easier to estimate classical correlations in quantum information theory.

Contribution

It defines measures of classical correlations that serve as computable upper bounds on the distillable randomness, addressing the difficulty of regularized quantity calculation.

Findings

Proves these measures are valid upper bounds.

Provides semi-definite programming methods for computation.

Evaluates bounds for isotropic quantum states.

Abstract

The distillable randomness of a bipartite quantum state is an information-theoretic quantity equal to the largest net rate at which shared randomness can be distilled from the state by means of local operations and classical communication. This quantity has been widely used as a measure of classical correlations, and one version of it is equal to the regularized Holevo information of the ensemble that results from measuring one share of the state. However, due to the regularization, the distillable randomness is difficult to compute in general. To address this problem, we define measures of classical correlations and prove a number of their properties, most importantly that they serve as upper bounds on the distillable randomness of an arbitrary bipartite state. We then further bound these measures from above by some that are efficiently computable by means of semi-definite programming, we evaluate one of them for the example of an isotropic state, and we remark on the relation to quantities previously proposed in the literature.