Quantum hypothesis testing with group symmetry

TL;DR

This paper investigates quantum hypothesis testing under symmetry constraints, analyzing asymptotic error bounds and comparing the effectiveness of group-invariant versus unrestricted measurements.

Contribution

It derives bounds on error exponents for symmetric quantum state discrimination and compares the performance of invariant and unrestricted measurement strategies.

Findings

Bounds on Chernoff, Hoeffding, and Stein error exponents for symmetric quantum states.

Group-invariant measurements can perform differently than unrestricted measurements in quantum hypothesis testing.

Theoretical insights into the role of symmetry in quantum state discrimination.

Abstract

The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with the problems of the Chernoff bound, the Hoeffding bound and Stein's lemma, and derive bounds on these quantities in terms of their corresponding statistical distance measures. A special emphasis is put on the comparison of the performances of group-invariant and unrestricted measurements.