Quantum-state comparison and discrimination

TL;DR

This paper analyzes quantum state comparison, revealing that the discrimination strategy is often suboptimal and proposing conditions under which it performs worse than no measurement, especially for multiple states.

Contribution

It provides a sufficient condition for when discrimination-based comparison is suboptimal and determines optimal success probabilities for two pure states with error margins.

Findings

Discrimination strategy can be worse than no measurement in some cases.

Optimal comparison success probability is derived for two pure states with error margins.

Discrimination strategy is only optimal in the minimum-error case.

Abstract

We investigate the performance of discrimination strategy in the comparison task of known quantum states. In the discrimination strategy, one infers whether or not two quantum systems are in the same state on the basis of the outcomes of separate discrimination measurements on each system. In some cases with more than two possible states, the optimal strategy in minimum-error comparison is that one should infer the two systems are in different states without any measurement, implying that the discrimination strategy performs worse than the trivial "no-measurement" strategy. We present a sufficient condition for this phenomenon to happen. For two pure states with equal prior probabilities, we determine the optimal comparison success probability with an error margin, which interpolates the minimum-error and unambiguous comparison. We find that the discrimination strategy is not optimal except for the minimum-error case.