Hypothesis testing for Gaussian states on bosonic lattices

Abstract

The asymptotic state discrimination problem with simple hypotheses is considered for a cubic lattice of bosons. A complete solution is provided for the problems of the Chernoff and the Hoeffding bounds and Stein's lemma in the case when both hypotheses are gauge-invariant Gaussian states with translation-invariant quasi-free parts.

22 pages, submitted version

References in corpus (13)

• The Quantum Chernoff Bound
• Asymptotic Error Rates in Quantum Hypothesis Testing
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• Computable bounds for the discrimination of Gaussian states
• The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states
• Optimal sequence of quantum measurements in the sense of Stein's lemma in quantum hypothesis testing
• The Converse Part of The Theorem for Quantum Hoeffding Bound
• Error exponents in hypothesis testing for correlated states on a spin chain
• Large deviations and Chernoff bound for certain correlated states on a spin chain
• An Ergodic Theorem for the Quantum Relative Entropy
• Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems
• Quantum Stein's lemma revisited, inequalities for quantum entropies, and a concavity theorem of Lieb
• Large Deviations in Quantum Spin Chain

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• Discriminating quantum states: the multiple Chernoff distance
• Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination
• Coding theorems for compound problems via quantum Rényi divergences
• Quantum hypothesis testing with group symmetry
• Second-order asymptotics for quantum hypothesis testing in settings beyond i.i.d. - quantum lattice systems and more
• Two approaches to obtain the strong converse exponent of quantum hypothesis testing for general sequences of quantum states
• Probing light polarization with the quantum Chernoff bound
• Local hypothesis testing between a pure bipartite state and the white noise state
• Quantum hypothesis testing for quantum Gaussian states: Quantum analogues of chi-square, t and F tests
• Quantum $f$-divergences via Nussbaum-Szkoła Distributions and Applications to $f$-divergence Inequalities
• Petz-Rényi Relative Entropy of Thermal States and their Displacements
• Relative Entropy via Distribution of Observables
• Asymptotic Convertibility of Entanglement: A General Approach to Entanglement Concentration and Dilution