Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics

Abstract

We extend the mathematical theory of quantum hypothesis testing to the general $W^{\ast }$-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.

60 pages

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• The Quantum Chernoff Bound
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Dissipative Transport: Thermal Contacts and Tunnelling Junctions
• Error exponents in hypothesis testing for correlated states on a spin chain
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• Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems
• Theory of Non-Equilibrium Sationary States as a Theory of Resonances
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• Hypothesis testing for Gaussian states on bosonic lattices
• Typical support and Sanov large deviations of correlated states
• Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems
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Cited by in corpus (35)

• Converse bounds for private communication over quantum channels
• Gaussian hypothesis testing and quantum illumination
• Quantum correlations and distinguishability of quantum states
• Entropic fluctuations of quantum dynamical semigroups
• Rényi divergences as weighted non-commutative vector valued $L_p$-spaces
• Rényi relative entropies and noncommutative $L_p$-spaces
• On entropy production of repeated quantum measurements I. General theory
• Applications of position-based coding to classical communication over quantum channels
• Upper bounds on secret key agreement over lossy thermal bosonic channels
• Quantum state discrimination bounds for finite sample size
• Sanov and Central Limit Theorems for output statistics of quantum Markov chains
• Coding theorems for compound problems via quantum Rényi divergences
• Second-order asymptotics for quantum hypothesis testing in settings beyond i.i.d. - quantum lattice systems and more
• On entropy production of repeated quantum measurements II. Examples
• On the steady state correlation functions of open interacting systems
• Large Deviations and Fluctuation Theorem for Selectively Decoupled Measures on Shift Spaces
• Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels
• A note on the Landauer principle in quantum statistical mechanics
• Test-measured Rényi divergences
• The strong converse exponent of discriminating infinite-dimensional quantum states
• On the error exponents of binary state discrimination with composite hypotheses
• Landauer's Principle for Trajectories of Repeated Interaction Systems
• Relating relative Rényi entropies and Wigner-Yanase-Dyson skew information to generalized multiple quantum coherences
• Random paths and current fluctuations in nonequilibrium statistical mechanics
• Recurrence times, waiting times and universal entropy production estimators
• Contractivity properties of a quantum diffusion semigroup
• Quantum Rényi divergences and the strong converse exponent of state discrimination in operator algebras
• Quantum $f$-divergences via Nussbaum-Szkoła Distributions and Applications to $f$-divergence Inequalities
• Entropic Fluctuations in Statistical Mechanics II. Quantum Dynamical Systems
• Relative Entropy via Distribution of Observables
• The large-time and vanishing-noise limits for entropy production in nondegenerate diffusions
• Asymptotic Equipartition Theorems in von Neumann algebras
• Quenched large deviations of Birkhoff sums along random quantum measurements
• Classical capacities of memoryless but not identical quantum channels
• Miniatures on Open Quantum Systems