PreprintCC BY 4.0arXiv
Quantum Channel Stein Theorem beyond Definite Causal Order
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∈(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.
Related
- Geometric Rényi divergence and RLD Fisher information under quantum processes without definite causal order
- Unbounded separation between definite and indefinite causal order in finite-dimensional quantum metrology
- Quantum Foundations Beyond Bell's Theorem: A Topical Review
- The finite key effect of side-channel-secure quantum key distribution beyond post-selection technique
- Fundamental Limits of Quantum Metrology Beyond Fixed Causal Order
BibTeX
@misc{zhu2026quantum,
title = {{Quantum Channel Stein Theorem beyond Definite Causal Order}},
author = {Chengkai Zhu and Xin Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30268},
eprint = {2609.30268},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30268},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Channel Stein Theorem beyond Definite Causal Order
AU - Chengkai Zhu
AU - Xin Wang
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30268
UR - https://arxiv.org/abs/2609.30268
AB - 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∈(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.
ER -