Optimal quantum state discrimination with fixed measurements

Researchers in the Quantum neXus Laboratory (QX Lab) establish a mathematical foundation for quantum state discrimination in physical scenarios where the measurement apparatus is fixed. The research received a Best Paper Award at the 2025 International Conference on Quantum Communications.

Authors: Maison Clouâtré, Stefano Marano, Andrea Conti, Peter L. Falb, and Moe Z. Win
Citation: Proc. Int. Conf. on Quantum Commun., Netw., and Comput. (QCNC), Nara, Japan, Apr. 2025, pp. 247–253

Abstract:
Given an unknown quantum state described by one of two possible density operators, the Helstrom bound provides the minimum discrimination error probability (DEP) by optimizing over all possible quantum measurements. However, it is unrealistic to implement arbitrary measurements in practice due to physical limitations of measurement apparatuses. This paper considers a quantum state discrimination scenario where a fixed measurement apparatus is available. In this setting, we advocate the use of quantum pre-processing (QPP) to realize effectively different measurements from that of the fixed apparatus. Applying optimal QPP prior to measurement with the fixed apparatus allows one to minimize the DEP. This paper derives the minimum DEP, determines the QPP required to achieve it, and provides necessary and sufficient conditions for this minimum DEP with optimal QPP to coincide with the Helstrom bound.