A quantum version of Sanov's theorem

Abstract

We present a quantum extension of a version of Sanov's theorem focussing on a hypothesis testing aspect of the theorem: There exists a sequence of typical subspaces for a given set $\Psi$ of stationary quantum product states asymptotically separating them from another fixed stationary product state. Analogously to the classical case, the exponential separating rate is equal to the infimum of the quantum relative entropy with respect to the quantum reference state over the set $\Psi$. However, while in the classical case the separating subsets can be chosen universal, in the sense that they depend only on the chosen set of i.i.d. processes, in the quantum case the choice of the separating subspaces depends additionally on the reference state.

15 pages

References in corpus (1)

• Chained Typical Subspaces - a Quantum Version of Breiman's Theorem

Cited by in corpus (46)

• The large deviation approach to statistical mechanics
• Asymptotic Error Rates in Quantum Hypothesis Testing
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
• Second-order asymptotics for quantum hypothesis testing
• A Generalization of Quantum Stein's Lemma
• Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution
• Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
• Universal coding for classical-quantum channel
• Discriminating quantum states: the multiple Chernoff distance
• Tight bound on relative entropy by entropy difference
• A selection of nonequilibrium issues
• Reflection positivity and phase transitions in lattice spin models
• Applications of position-based coding to classical communication over quantum channels
• Large deviations and Chernoff bound for certain correlated states on a spin chain
• On Composite Quantum Hypothesis Testing
• Distinguishing Random and Black Hole Microstates
• Sanov and Central Limit Theorems for output statistics of quantum Markov chains
• Quantification of correlations in quantum many-particle systems
• Coding theorems for compound problems via quantum Rényi divergences
• Typical support and Sanov large deviations of correlated states
• Hypothesis Testing on Invariant Subspaces of the Symmetric Group, Part I - Quantum Sanov's Theorem and Arbitrarily Varying Sources
• Quantum hypothesis testing with group symmetry
• Classical Capacities of Averaged and Compound Quantum Channels
• Entanglement Theory and the Quantum Simulation of Many-Body Physics
• Quantum Macrostates, Equivalence of Ensembles and an H-Theorem
• Maximizing the divergence from a hierarchical model of quantum states
• A solution of the generalised quantum Stein's lemma
• Continuity of the Maximum-Entropy Inference
• Discrimination of quantum states under locality constraints in the many-copy setting
• Monotonic multi-state quantum $f$-divergences
• On the error exponents of binary state discrimination with composite hypotheses
• Local hypothesis testing between a pure bipartite state and the white noise state
• Deviation bounds and concentration inequalities for quantum noises
• A limit relation for entropy and channel capacity per unit cost
• Asymptotic relative submajorization of multiple-state boxes
• Black Box Work Extraction and Composite Hypothesis Testing
• Asymptotic quantification of entanglement with a single copy
• Measuring quantum relative entropy with finite-size effect
• Towards Quantum Universal Hypothesis Testing
• Categories of Brègman operations and epistemic (co)monads
• Appearance of Gibbs states in quantum-state tomography
• Universal tester for multiple independence testing and classical-quantum arbitrarily varying multiple access channel
• The Quantum Relative Entropy as a Rate Function and Information Criteria
• Large deviations in the quantum quasi-1D jellium
• Discrete-time classical and quantum Markovian evolutions: Maximum entropy problems on path space