Maximal Holevo quantity based on weak measurements

TL;DR

This paper introduces the weak maximal Holevo quantity, a generalization of the Holevo bound using weak measurements, applicable in scenarios with limited measurement strength, and evaluates it for Bell-diagonal states.

Contribution

It proposes the weak maximal Holevo quantity as a new measure and analyzes its properties for Bell-diagonal states, including realization via noise and projective measurements.

Findings

Weak measurements can be used to realize the weak maximal Holevo quantity.

The weak maximal Holevo quantity is systematically evaluated for Bell-diagonal states.

Weak measurements can be realized by noise and projective measurements.

Abstract

The Holevo bound is a keystone in many applications of quantum information theory. We propose "weak maximal Holevo quantity" with weak measurements as the generalization of the standard Holevo quantity which is defined as the optimal projective measurements. The scenarios that weak measurements is necessary are that only the weak measurements can be performed because for example the system is macroscopic or that one intentionally tries to do so such that the disturbance on the measured system can be controlled for example in quantum key distribution protocols. We evaluate systematically the weak maximal Holevo quantity for Bell-diagonal states and find a series of results. Furthermore, we find that weak measurements can be realized by noise and project measurements.