Error exponents in hypothesis testing for correlated states on a spin chain

Abstract

We study various error exponents in a binary hypothesis testing problem and extend recent results on the quantum Chernoff and Hoeffding bounds for product states to a setting when both the null-hypothesis and the counter-hypothesis can be correlated states on a spin chain. Our results apply to states satisfying a certain factorization property; typical examples are the global Gibbs states of translation-invariant finite-range interactions as well as certain finitely correlated states.

26 pages; discussions extended, 2 figures added

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• The structure of Renyi entropic inequalities
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• Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
• Resource theory of asymmetric distinguishability
• Reversibility conditions for quantum operations
• Rényi relative entropies and noncommutative $L_p$-spaces
• Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination
• Large deviations and Chernoff bound for certain correlated states on a spin chain
• Preservation of a quantum Renyi relative entropy implies existence of a recovery map
• Quantum state discrimination bounds for finite sample size
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• Quantum hypothesis testing with group symmetry
• The modified logarithmic Sobolev inequality for quantum spin systems: classical and commuting nearest neighbour interactions
• Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems
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• Two approaches to obtain the strong converse exponent of quantum hypothesis testing for general sequences of quantum states
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• The strong converse exponent of discriminating infinite-dimensional quantum states
• On the error exponents of binary state discrimination with composite hypotheses
• Local hypothesis testing between a pure bipartite state and the white noise state
• Quantum hypothesis testing in many-body systems
• Exponential error rates in multiple state discrimination on a quantum spin chain
• Quantum Rényi divergences and the strong converse exponent of state discrimination in operator algebras
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• Asymptotic Convertibility of Entanglement: A General Approach to Entanglement Concentration and Dilution
• Finite blocklength and moderate deviation analysis of hypothesis testing of correlated quantum states and application to classical-quantum channels with memory
• Super-exponential distinguishability of correlated quantum states