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

References in corpus (6)

• The Quantum Chernoff Bound
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• The Converse Part of The Theorem for Quantum Hoeffding Bound
• Large deviations in quantum lattice systems: one-phase region
• Large deviations and Chernoff bound for certain correlated states on a spin chain
• Typical support and Sanov large deviations of correlated states

Cited by in corpus (4)

• Generalized relative entropies and the capacity of classical-quantum channels
• Large deviations and Chernoff bound for certain correlated states on a spin chain
• Hypothesis testing for Gaussian states on bosonic lattices
• Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems