The Converse Part of The Theorem for Quantum Hoeffding Bound

Abstract

We prove the converse part of the theorem for quantum Hoeffding bound on the asymptotics of quantum hypothesis testing, essentially based on an argument developed by Nussbaum and Szkola in proving the converse part of the quantum Chernoff bound. Our result complements Hayashi's proof of the direct (achievability) part of the theorem, so that the quantum Hoeffding bound has now been established.

References in corpus (3)

• The Quantum Chernoff Bound
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• An Information-Spectrum Approach to Classical and Quantum Hypothesis Testing for Simple Hypotheses

Cited by in corpus (39)

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• An Information-Spectrum Approach to Classical and Quantum Hypothesis Testing for Simple Hypotheses
• Correlation Detection and an Operational Interpretation of the Renyi Mutual Information
• Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
• Gaussian hypothesis testing and quantum illumination
• Strong converse exponent for classical-quantum channel coding
• Relating different quantum generalizations of the conditional Renyi entropy
• Multiplicativity of completely bounded $p$-norms implies a strong converse for entanglement-assisted capacity
• Principles of Quantum Communication Theory: A Modern Approach
• Operational Interpretation of Renyi Information Measures via Composite Hypothesis Testing Against Product and Markov Distributions
• A smooth entropy approach to quantum hypothesis testing and the classical capacity of quantum channels
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• Reversibility conditions for quantum operations
• Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing
• Distinguishing Random and Black Hole Microstates
• Preservation of a quantum Renyi relative entropy implies existence of a recovery map
• Renyi relative entropies of quantum Gaussian states
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification
• Hypothesis testing for Gaussian states on bosonic lattices
• Constant Compositions in the Sphere Packing Bound for Classical-Quantum Channels
• Quantum hypothesis testing with group symmetry
• Usefulness of adaptive strategies in asymptotic quantum channel discrimination
• Second-order asymptotics for quantum hypothesis testing in settings beyond i.i.d. - quantum lattice systems and more
• Optimal Adaptive Strategies for Sequential Quantum Hypothesis Testing
• Test-measured Rényi divergences
• Tight asymptotic bounds on local hypothesis testing between a pure bipartite state and the white noise state
• Parallelization of Adaptive Quantum Channel Discrimination in the Non-Asymptotic Regime
• Some continuity properties of quantum Rényi divergences
• Quantum Rényi divergences and the strong converse exponent of state discrimination in operator algebras
• Quantifying the unextendibility of entanglement
• Moderate Deviation Analysis for Classical-Quantum Channels and Quantum Hypothesis Testing
• Quantum $f$-divergences via Nussbaum-Szkoła Distributions and Applications to $f$-divergence Inequalities
• Sphere-Packing Bound for Symmetric Classical-Quantum Channels
• Interpolating between symmetric and asymmetric hypothesis testing
• The Quantum Relative Entropy as a Rate Function and Information Criteria