Optimal Quantum State Discrimination with Fixed Measurements

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.