2017/05/31 by Nengkun Yu, Li Zhou
Computer Science · Physics and Astronomy · #Chernoff bound #Exponent #Probability distribution #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum algorithm #Quantum capacity #Quantum information #Upper and lower bounds #quant-ph
paper · pdf · doi:10.1109/tit.2021.3067924
published as IEEE Transactions on Information Theory ( Volume: 67, Issue: 7, July 2021) · Comments are welcome
openalex publication_date 2021/03/22 · openalex created_date 2021/03/29 · arxiv created 2022/01/25 · arxiv updated 2022/01/26 · openalex updated_date 2026/08/05
We consider the problem of testing two hypotheses of quantum operations in a setting of many uses where an arbitrary prior probability distribution is given. The Chernoff exponent for quantum operations is investigated to track the minimal average error probability of discriminating two quantum operations asymptotically. We answer the question, “When is the Chernoff exponent for quantum operations finite?” We show that either two quantum operations can be perfectly distinguished with finite uses, or the minimal discrimination error decays exponentially with respect to the number of uses asymptotically. That is, the Chernoff exponent is finite if and only if the quantum operations can not be perfectly distinguished with finite uses. This rules out the possibility of super-exponential decay of error probability. Upper bounds of the Chernoff exponent for quantum operations are provided.