Distinguishability, classical information of quantum operations

TL;DR

This paper extends measures of distinguishability from pure states to mixed states and quantum operations, providing formulas and demonstrating paradoxes in quantum information distinguishability.

Contribution

It introduces self-consistent measures of distinguishability for mixed states and quantum operations, and derives an exact formula for SU(2) ensembles.

Findings

Generalized fidelity and von Neumann entropy to quantum operations

Constructed an additive Holevo quantity for quantum operations

Demonstrated the Jozsa-Schlienz paradox in quantum operations

Abstract

A basic property of distinguishability is that it is non-increasing under further quantum operations. Following this, we generalize two measures of distinguishability of pure states--fidelity and von Neumann entropy, to mixed states as self-consistent measures. Then we extend these two measures to quantum operations. The information-theoretic point of the generalized Holevo quantity of an ensemble of quantum operations is constructed. Preferably it is an additive measure. The exact formula for SU(2) ensemble is presented. With the aid of the formula, we show Jozsa-Schlienz paradox that states as a whole are less distinguishable while all pairwise are more distinguishable in an ensemble of quantum states, also occurs in an ensemble of quantum operations, even in the minimal dimensional case SU(2) ensemble.