TY - JOUR

T1 - Amortized channel divergence for asymptotic quantum channel discrimination

AU - Wilde, Mark M.

AU - Berta, Mario

AU - Hirche, Christoph

AU - Kaur, Eneet

N1 - Funding Information: We are grateful to Fernando Brandão, Gilad Gour, Milan Mosonyi, Giacomo de Palma and Andreas Winter for discussions related to the topic of this paper. The authors would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme “Beyond i.i.d. in information theory,” which was supported by EPSRC Grant Number EP/R014604/1. CH acknowledges support from Spanish MINECO, project FIS2016-80681-P with the support of AEI/FEDER funds and FPI Grant No. BES-2014-068888, as well as by the Generalitat de Catalunya, project CIRIT 2017-SGR-1127. EK acknowledges support from the Office of Naval Research. MMW acknowledges support from the National Science Foundation under Grant No. 1907615. He is also grateful to MB for hosting him for research discussions at Imperial College London during May 2018.

PY - 2020/6/18

Y1 - 2020/6/18

N2 - 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. arXiv:0804.0686) 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.

AB - 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. arXiv:0804.0686) 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.

KW - Amortized channel divergence

KW - Error exponent

KW - Quantum channel discrimination

KW - Strong converse exponent

UR - http://www.scopus.com/inward/record.url?scp=85086659601&partnerID=8YFLogxK

U2 - 10.1007/s11005-020-01297-7

DO - 10.1007/s11005-020-01297-7

M3 - Article

AN - SCOPUS:85086659601

VL - 110

SP - 2277

EP - 2336

JO - Letters in mathematical physics

JF - Letters in mathematical physics

SN - 0377-9017

IS - 8

ER -