The optimal positive operator-valued measure for state discrimination

TL;DR

This paper derives the optimal positive operator-valued measure (POVM) for discriminating non-orthogonal quantum states, providing a tighter bound than Holevo's, with implications for quantum key distribution security.

Contribution

The paper introduces a generalized POVM measurement and derives the optimal measurement for state discrimination using Lagrange multipliers.

Findings

Optimal POVM provides a tight upper bound for state discrimination.

Optimal measurement significantly improves over Holevo bound.

Results have implications for quantum key distribution security.

Abstract

Evaluating the amount of information obtained from non-orthogonal quantum states is an important topic in the field of quantum information. The commonly used evaluation method is Holevo bound, which only provides a loose upper bound for quantum measurement. In this paper, we provide a theoretical study of the positive operator-valued measure (POVM) for discriminating nonorthogonal states. We construct a generalized POVM measurement operation, and derive the optimal one for state discrimination by Lagrange multiplier method. With simulation, we find that the optimal POVM measurement provides a tight upper bound for state discrimination, which is significantly lower than that predicted by Holevo bound. The derivation of optimal POVM measurement will play an important role in the security research of quantum key distribution.