Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding

Abstract

In the simple quantum hypothesis testing problem, upper bound with asymmetric setting is shown by using a quite useful inequality by Audenaert et al, quant-ph/0610027, which was originally invented for symmetric setting. Using this upper bound, we obtain the Hoeffding bound, which are identical with the classical counter part if the hypotheses, composed of two density operators, are mutually commutative. Our upper bound improves the bound by Ogawa-Hayashi, and also provides a simpler proof of the direct part of the quantum Stein's lemma. Further, using this bound, we obtain a better exponential upper bound of the average error probability of classical-quantum channel coding.

References in corpus (2)

• The Quantum Chernoff Bound
• Exponents of quantum fixed-length pure state source coding

Cited by in corpus (113)

• Quantum channels and memory effects
• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• One-Shot Classical-Quantum Capacity and Hypothesis Testing
• Asymptotic Error Rates in Quantum Hypothesis Testing
• Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
• Quantum f-divergences and error correction
• Second-order asymptotics for quantum hypothesis testing
• On the quantum Renyi relative entropies and related capacity formulas
• An Information-Spectrum Approach to Classical and Quantum Hypothesis Testing for Simple Hypotheses
• Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication
• A Generalization of Quantum Stein's Lemma
• Correlation Detection and an Operational Interpretation of the Renyi Mutual Information
• Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
• Different quantum f-divergences and the reversibility of quantum operations
• Gaussian hypothesis testing and quantum illumination
• Strong converse exponent for classical-quantum channel coding
• Discrimination of two channels by adaptive methods and its application to quantum system
• Multiplicativity of completely bounded $p$-norms implies a strong converse for entanglement-assisted capacity
• Quantum secure direct communication with private dense coding using general preshared quantum state
• Principles of Quantum Communication Theory: A Modern Approach
• The Converse Part of The Theorem for Quantum Hoeffding Bound
• Lower bounds on the Probability of Error for Classical and Classical-Quantum Channels
• The structure of Renyi entropic inequalities
• Generalized relative entropies and the capacity of classical-quantum channels
• Quantum Relative Lorenz Curves
• Resource theory of asymmetric distinguishability
• Universal coding for classical-quantum channel
• A smooth entropy approach to quantum hypothesis testing and the classical capacity of quantum channels
• Error exponents in hypothesis testing for correlated states on a spin chain
• Entropy of a quantum channel
• A limit of the quantum Renyi divergence
• Quantum wiretap channel with non-uniform random number and its exponent and equivocation rate of leaked information
• Reversibility conditions for quantum operations
• Optimized quantum f-divergences and data processing
• Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing
• Sequential projective measurements for channel decoding
• Moderate deviation analysis for classical communication over quantum channels
• Achieving the Holevo bound via sequential measurements
• Applications of position-based coding to classical communication over quantum channels
• Large deviation analysis for quantum security via smoothing of Renyi entropy of order 2
• Quantum Sequential Hypothesis Testing
• Distinguishing Random and Black Hole Microstates
• Preservation of a quantum Renyi relative entropy implies existence of a recovery map
• Quantum state discrimination bounds for finite sample size
• Rényi generalizations of quantum information measures
• Renyi relative entropies of quantum Gaussian states
• Non-Asymptotic Classical Data Compression with Quantum Side Information
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification
• Divergence radii and the strong converse exponent of classical-quantum channel coding with constant compositions
• Hypothesis testing for Gaussian states on bosonic lattices
• Multi-Phase Hadamard receivers for classical communication on lossy bosonic channels
• Optimally controlled quantum discrimination and estimation
• Coding theorems for compound problems via quantum Rényi divergences
• Quantum hypothesis testing with group symmetry
• Usefulness of adaptive strategies in asymptotic quantum channel discrimination
• Entanglement Theory and the Quantum Simulation of Many-Body Physics
• Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems
• Achieving the Holevo bound via a bisection decoding protocol
• Second-order asymptotics for quantum hypothesis testing in settings beyond i.i.d. - quantum lattice systems and more
• Properties of Noncommutative Renyi and Augustin Information
• Optimal protocols for quantum metrology with noisy measurements
• The capacity of coherent-state adaptive decoders with interferometry and single-mode detectors
• Strong converse exponents for the feedback-assisted classical capacity of entanglement-breaking channels
• Two approaches to obtain the strong converse exponent of quantum hypothesis testing for general sequences of quantum states
• Recoverability for optimized quantum $f$-divergences
• Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels
• 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
• Dense Coding with Locality Restriction for Decoder: Quantum Encoders vs. Super-Quantum Encoders
• Asymptotic local hypothesis testing between a pure bipartite state and the completely mixed state
• The strong converse exponent of discriminating infinite-dimensional quantum states
• Strong converses for group testing in the finite blocklength regime
• Parallelization of Adaptive Quantum Channel Discrimination in the Non-Asymptotic Regime
• On the error exponents of binary state discrimination with composite hypotheses
• Some continuity properties of quantum Rényi divergences
• Secure communication over fully quantum Gel'fand-Pinsker wiretap channel
• Duality between source coding with quantum side information and c-q channel coding
• Finite-Length Analyses for Source and Channel Coding on Markov Chains
• Geometric relative entropies and barycentric Rényi divergences
• Reliability Function of Classical-Quantum Channels
• A hypothesis testing approach for communication over entanglement assisted compound quantum channel
• An invitation to the sample complexity of quantum hypothesis testing
• Tight lower bound on the error exponent of classical-quantum channels
• Moderate Deviation Analysis for Classical-Quantum Channels and Quantum Hypothesis Testing
• Quantifying the unextendibility of entanglement
• Reliable Simulation of Quantum Channels: the Error Exponent
• Non-Asymptotic Analysis of Privacy Amplification via Renyi Entropy and Inf-Spectral Entropy
• Quantum hypothesis testing for quantum Gaussian states: Quantum analogues of chi-square, t and F tests
• Quantum Rényi divergences and the strong converse exponent of state discrimination in operator algebras
• Lower Bounds on Error Exponents via a New Quantum Decoder
• Quantum illumination with noisy probes: Conditional advantages of non-Gaussianity
• Achievable error exponents of data compression with quantum side information and communication over symmetric classical-quantum channels
• A strong converse bound for multiple hypothesis testing, with applications to high-dimensional estimation
• Discrimination power of a quantum detector
• Quantum $f$-divergences via Nussbaum-Szkoła Distributions and Applications to $f$-divergence Inequalities
• Quantum dichotomies and coherent thermodynamics beyond first-order asymptotics
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
• Analytical bounds for non-asymptotic asymmetric state discrimination
• Capacity of optical reading, Part 1: Reading boundless error-free bits using a single photon
• On distinguishability distillation and dilution exponents
• Towards the ultimate limits of quantum channel discrimination and quantum communication
• Finite blocklength and moderate deviation analysis of hypothesis testing of correlated quantum states and application to classical-quantum channels with memory
• Interpolating between symmetric and asymmetric hypothesis testing
• Towards Quantum Universal Hypothesis Testing
• Optimized quantum f-divergences
• Quantum hypothesis testing between qubit states with parity
• Random coding exponents galore via decoupling
• The Quantum Relative Entropy as a Rate Function and Information Criteria
• Two-way classical communication remarkably improves local distinguishability
• Enhanced quantum hypothesis testing via the interplay between coherent evolution and noises
• Super-exponential distinguishability of correlated quantum states
• Tight relations and equivalences between smooth relative entropies