Qubit State Discrimination using Post-measurement Information

TL;DR

This paper analyzes the optimal strategies for discriminating nonorthogonal qubit states when post-measurement information is available, revealing structural properties and conditions for null measurements.

Contribution

It provides an analytic framework for optimal measurements and characterizes when null measurements are optimal in qubit state discrimination with post-measurement information.

Findings

Optimal measurement structure derived analytically.

Null optimal measurement always exists with post-measurement info.

Explicit optimal probability for four-state discrimination obtained.

Abstract

We consider the optimal discrimination of nonorthogonal qubit states with post-measurement information and provide an analytic structure of the optimal measurements. We also show that there is always a null optimal measurement when post-measurement information is given. Further, in discriminating four states using post-measurement information, we analytically provide the optimal probability of correct guessing and show that the uniqueness of optimal measurement is equivalent to the non-existence of non-null optimal measurement with post-measurement information.