期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 61, 期 12, 页码 6975-6994出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2015.2489259
关键词
Hypothesis testing; Renyi divergences; correlated quantum states
资金
- European Research Council through Advanced Grant IRQUAT
- Ministry of Education, Culture, Sports, Science, and Technology
- Spanish MINECO Project [FIS2013-40627-P]
- Generalitat de Catalunya CIRIT Project [2014 SGR 966]
- Institute for Advanced Study, Technische Universitat Munchen - German Excellence Initiative
- European Union Seventh Framework Programme [291763]
- Project on Multi-User Quantum Network [20686026]
We present two general approaches to obtain the strong converse exponent of simple quantum hypothesis testing for correlated quantum states. One approach requires that the states satisfy a certain factorization property; typical examples of such states are the temperature states of translation-invariant finite-range interactions on a spin chain. The other approach requires the differentiability of a regularized Renyi alpha-divergence in the parameter a; typical examples of such states include temperature states of non-interacting fermionic lattice systems, and classical irreducible Markov chains. In all cases, we get that the strong converse exponent is equal to the Hoeffding anti-divergence, which in turn is obtained from the regularized Renyi divergences of the two states.
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