# Sequential Discrimination of Mixed Quantum States

## TL;DR

This paper explores how mixed quantum states can outperform pure states in sequential discrimination under equal fidelity conditions.

## Contribution

The study reveals that mixed states can achieve higher success probabilities in sequential discrimination compared to pure states.

## Key findings

- Mixed-state protocols show higher success probability than pure-state ones under equal fidelity.
- The difference in performance increases with the mixability of the initial states.
- Classical communication reverses the success probability advantage in favor of pure states.

## Abstract

Classical mixtures of quantum states often give rise to decoherence and are generally considered detrimental to quantum processing. However, in the framework of sequential measurement, such mixtures can be beneficial for state discrimination. We investigate the sequential discrimination of mixed states and compare the results with those of pure states under the condition of equal fidelity. It is found that the successful probability of the mixed-state protocol is superior to the pure one under the equal-fidelity condition. It is shown that the difference between the sequential discrimination of pure and mixed states is more reliable under the equal-fidelity condition than under single-shot discrimination, and this difference increases with the mixability of the initial mixed states. For scenarios in which classical communication is allowed, the optimal successful probability of pure-state discriminations is larger than that for mixed states on the contrary. We also show that the classical mixture of basic vectors from quantum decoherence has a subtle impact on the communication channel induced by the coincidence of the maximal mutual information and optimal successful probability of sequential discrimination for pure states.