期刊
PHYSICAL REVIEW A
卷 105, 期 2, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.105.022419
关键词
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资金
- Peng Cheng Laboratory (PCL)
- DFG cluster of excellence 2111 (Munich Center for Quantum Science and Technology)
- Baidu-UAB collaborative project Learning of Quantum Hidden Markov Models
- Spanish MINECO [FIS2016-86681-P, PID2019107609GB-I00/AEI/10.13039/501100011033]
- FEDER funds
- Generalitat de Catalunya [2017-SGR-1127]
- Catalan Government within the ERDF Program of Catalunya [001-P-001644]
- Guangdong Provincial Key Laboratory [2019B121203002]
- JSPS [17H01280, 16KT0017]
- Kayamori Foundation of Information Science Advancement
Adaptiveness is a key principle in information processing, and this study investigates its usefulness in asymptotic binary hypothesis testing for quantum channels. The results show that adaptive and nonadaptive strategies have the same error exponents for classical-quantum channels, and adaptive strategies do not outperform nonadaptive strategies when restricted to classical feed-forward and product state channel inputs.
Adaptiveness is a key principle in information processing including statistics and machine learning. We investigate the usefulness adaptive methods in the framework of asymptotic binary hypothesis testing, when each hypothesis represents asymptotically many independent instances of a quantum channel, and the tests are based on using the unknown channel and observing outputs. Unlike the familiar setting of quantum states as hypotheses, there is a fundamental distinction between adaptive and nonadaptive strategies with respect to the channel uses, and we introduce a number of further variants of the discrimination tasks by imposing different restrictions on the test strategies. The following results are obtained: (1) We prove that for classical-quantum channels, adaptive and nonadaptive strategies lead to the same error exponents both in the symmetric (Chernoff) and asymmetric (Hoeffding, Stein) settings. (2) The first separation between adaptive and nonadaptive symmetric hypothesis testing exponents for quantum channels, which we derive from a general lower bound on the error probability for nonadaptive strategies; the concrete example we analyze is a pair of entanglement-breaking channels. (3) We prove, in some sense generalizing the previous statement, that for general channels adaptive strategies restricted to classical feed-forward and product state channel inputs are not superior in the asymptotic limit to nonadaptive product state strategies. (4) As an application of our findings, we address the discrimination power of an arbitrary quantum channel and show that adaptive strategies with classical feedback and no quantum memory at the input do not increase the discrimination power of the channel beyond nonadaptive tensor product input strategies.
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