Researchers have determined the optimal universal coefficient for reducing multiple quantum hypothesis testing to binary tests. They have shown that the error probability of a global Pretty Good Measurement (PGM) is at most four times the sum of the optimal binary error probabilities. This result holds for any finite ensemble of quantum states in any Hilbert space dimension, whether finite or infinite. Furthermore, by constructing a family of regular-simplex ensembles, they have proven that this coefficient of four is optimal, even when considering arbitrary global measurements.

This finding improves upon previous pairwise bounds established by Cheng and Liu, providing an explicit and sharp guarantee for the standard PGM itself. The methodology employed is simpler than prior approaches, avoiding the construction of sequential measurements and the use of union bounds. Instead, the team relied on purely matrix-analytic techniques, combining a direct block Gram matrix analysis of the PGM error with a refined inequality between quantum Hellinger distance and Bures χ²-divergence.

Their analysis also yielded a refined, one-shot pairwise Chernoff bound and an explicit sufficient number of copies required to achieve a desired discrimination error. This advancement has significant implications for the efficiency and precision of quantum state discrimination, a fundamental pillar in quantum computing and quantum metrology, where the ability to distinguish between different quantum states with the lowest possible error probability is crucial.