Quantum hypothesis testing and state discrimination

TL;DR

This paper provides an overview of quantum hypothesis testing, discussing optimal measurement strategies, bounds on error probabilities, and the role of entanglement in quantum state and channel discrimination.

Contribution

It offers a comprehensive summary of the current theoretical understanding of quantum hypothesis testing and state discrimination, including bounds and strategies.

Findings

Optimal measurement strategies minimize error probability.

Entanglement enhances quantum channel discrimination.

Bounds on error probabilities guide measurement strategy design.

Abstract

This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error probability, is discussed. Collective and individual adaptive measurement strategies in testing hypotheses in the multiple copy scenario, with various upper and lower bounds on error probability, are outlined. A brief account on quantum channel discrimination and the role of entangled states in achieving enhanced precision in the task of channel discrimination is given.