期刊
LETTERS IN MATHEMATICAL PHYSICS
卷 110, 期 8, 页码 2277-2336出版社
SPRINGER
DOI: 10.1007/s11005-020-01297-7
关键词
Quantum channel discrimination; Amortized channel divergence; Error exponent; Strong converse exponent
资金
- Isaac Newton Institute for Mathematical Sciences
- EPSRC [EP/R014604/1]
- Spanish MINECO [FIS2016-80681-P]
- AEI/FEDER funds
- FPI [BES-2014-068888]
- Generalitat de Catalunya [CIRIT 2017-SGR-1127]
- Office of Naval Research
- National Science Foundation [1907615]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [1907615] Funding Source: National Science Foundation
It is well known that for the discrimination of classical and quantum channels in the finite, non-asymptotic regime, adaptive strategies can give an advantage over non-adaptive strategies. However, Hayashi (IEEE Trans Inf Theory 55(8):3807-3820, 2009.) showed that in the asymptotic regime, the exponential error rate for the discrimination of classical channels is not improved in the adaptive setting. We extend this result in several ways. First, we establish the strong Stein's lemma for classical-quantum channels by showing that asymptotically the exponential error rate for classical-quantum channel discrimination is not improved by adaptive strategies. Second, we recover many other classes of channels for which adaptive strategies do not lead to an asymptotic advantage. Third, we give various converse bounds on the power of adaptive protocols for general asymptotic quantum channel discrimination. Intriguingly, it remains open whether adaptive protocols can improve the exponential error rate for quantum channel discrimination in the asymmetric Stein setting. Our proofs are based on the concept of amortized distinguishability of quantum channels, which we analyse using data-processing inequalities.
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