# Optimal sequential measurements for bi-partite state discrimination

## TL;DR

This paper investigates when sequential measurements on bipartite quantum systems can match the performance of optimal joint measurements in state discrimination, providing conditions and comparisons to understand their effectiveness.

## Contribution

It derives conditions for optimal sequential measurements in bipartite state discrimination, analogous to Helstrom conditions, and compares their performance to joint measurements.

## Key findings

- Sequential measurements can sometimes match joint measurement performance.
- Derived conditions for optimal sequential measurements.
- Compared success probabilities of global vs. sequential strategies.

## Abstract

State discrimination is a useful test problem with which to clarify the power and limitations of different classes of measurement. We consider the problem of discriminating between given states of a bi-partite quantum system via sequential measurement of the subsystems, with classical feed-forward of measurement results. Our aim is to understand when sequential measurements, which are relatively easy to implement experimentally, perform as well, or almost as well as optimal joint measurements, which are in general more technologically challenging. We construct conditions that the optimal sequential measurement must satisfy, analogous to the well-known Helstrom conditions for minimum error discrimination in the unrestricted case. We give several examples and compare the optimal probability of correctly identifying the state via global versus sequential measurement strategies.