Year: 2026
Type: preprint
Abstract: Distinguishability is a central concept in information theory and extends naturally to quantum systems. This work shows that, for any two finite-dimensional memoryless quantum channels, parallel, adaptive and general testing strategies achieve the same Stein exponent at every fixed type-I error tolerance $ε\in(0,1)$, namely the regularized channel relative entropy. When this rate is finite, any larger type-II exponent forces the probability of correctly accepting the null hypothesis to decay exponentially. Thus, adaptivity provides no asymptotic advantage. The key step is proving the continuity of the regularized sandwiched Rényi channel divergence at order one. We also derive the exact strong-converse exponent for general testers.
Source: arXiv (Cornell University)
Authors: Zhu, Chengkai, Wang, Xin
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G2052179644, G8274973648
OpenAlex ID: W7214354887