Optimal error exponents for universal correlation detection

Determine whether the universal correlation detectors for fully quantum and classical–quantum states achieve the optimal type-I error exponent when the type-II error exponent is constrained.

Background

The paper constructs universal correlation detectors that attain the optimal first-order asymptotic performance without complete knowledge of the tested state. However, the authors note that the achievable type-I error exponent in both the fully quantum and classical–quantum settings is not known to be optimal. Resolving this would extend the first-order universality result to the finer error-exponent regime and determine whether state-agnostic detectors can match state-aware hypothesis-testing performance beyond the asymptotic rate.

References

On the other hand, in either the fully quantum case or the classical-quantum case in Proposition\ref{pro: universal correlation detection cq} and Proposition\ref{pro: semi universal detector}, the error exponent of the type I error is not optimal. At this point, it is not clear whether the universal correlation detectors above also achieve the optimal error exponent.

— All you need is the universal correlation detector: A unified approach to universalize communication protocols over quantum channels  (2609.29954 - Watanabe et al., 24 Sep 2026) in Section 3, subsection “Semi-universal correlation detection for fully quantum states”