An Information-Spectrum Approach to Classical and Quantum Hypothesis Testing for Simple Hypotheses

Abstract

The information-spectrum analysis made by Han for classical hypothesis testing for simple hypotheses is extended to a unifying framework including both classical and quantum hypothesis testing as well as fixed-length source coding, whereby general formulas for several quantities concerning the asymptotic optimality of tests/codes are established in terms of classical and quantum information spectrum. Generality of theorems and simplicity of proofs are fully pursued, and as byproducts some improvements on the original classical results are also obtained.

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References in corpus (8)

• The Quantum Chernoff Bound
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• 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
• A quantum version of Sanov's theorem
• Exponents of quantum fixed-length pure state source coding
• General formulas for fixed-length quantum entanglement concentration
• Optimal sequence of POVMs in the sense of Stein's lemma in quantum hypothesis testing

Cited by in corpus (67)

• Min- and Max- Relative Entropies and a New Entanglement Monotone
• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
• Duality Between Smooth Min- and Max-Entropies
• Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
• The quantum capacity of channels with arbitrarily correlated noise
• Second-order asymptotics for quantum hypothesis testing
• Polar codes for classical-quantum channels
• A Generalization of Quantum Stein's Lemma
• Correlation Detection and an Operational Interpretation of the Renyi Mutual Information
• Strong converse exponent for classical-quantum channel coding
• Smooth Renyi Entropies and the Quantum Information Spectrum
• Discrimination of two channels by adaptive methods and its application to quantum system
• One shot entanglement assisted classical and quantum communication over noisy quantum channels: A hypothesis testing and convex split approach
• The Converse Part of The Theorem for Quantum Hoeffding Bound
• Quantum thermodynamics of correlated-catalytic state conversion at small-scale
• Distilling entanglement from arbitrary resources
• Operational Interpretation of Renyi Information Measures via Composite Hypothesis Testing Against Product and Markov Distributions
• Entanglement cost in practical scenarios
• Smooth Max-Information as One-Shot Generalization for Mutual Information
• Second-order asymptotics for source coding, dense coding and pure-state entanglement conversions
• A smooth entropy approach to quantum hypothesis testing and the classical capacity of quantum channels
• Generalized Entropies
• Error exponents in hypothesis testing for correlated states on a spin chain
• Catalytic Decoupling of Quantum Information
• Quantum Sphere-Packing Bounds with Polynomial Prefactors
• 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
• Covert Capacity of Bosonic Channels
• Quantum state discrimination bounds for finite sample size
• Reverse Test and Characterization of Quantum Relative Entropy
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification
• Typical support and Sanov large deviations of correlated states
• A generalized quantum Slepian-Wolf
• Quantum hypothesis testing with group symmetry
• Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems
• Two approaches to obtain the strong converse exponent of quantum hypothesis testing for general sequences of quantum states
• Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems
• Moderate deviation expansion for fully quantum tasks
• Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels
• Tight asymptotic bounds on local hypothesis testing between a pure bipartite state and the white noise state
• One-shot Capacity bounds on the Simultaneous Transmission of Classical and Quantum Information
• Quantum Coding Theorems for Arbitrary Sources, Channels and Entanglement Resources
• Discrimination of quantum states under locality constraints in the many-copy setting
• On the error exponents of binary state discrimination with composite hypotheses
• Secure communication over fully quantum Gel'fand-Pinsker wiretap channel
• Local hypothesis testing between a pure bipartite state and the white noise state
• The block-coherence measures and the coherence measures based on positive-operator-valued measures
• Finite-Block-Length Analysis in Classical and Quantum Information Theory
• Capacity with energy constraint in coherent state channel
• Asymptotic Reversibility of Thermal Operations for Interacting Quantum Spin Systems via Generalized Quantum Stein's Lemma
• Multiple Quantum Hypothesis Testing Expressions and Classical-Quantum Channel Converse Bounds
• Strong Converse and Second-Order Asymptotics of Channel Resolvability
• Moderate Deviation Analysis for Classical-Quantum Channels and Quantum Hypothesis Testing
• Beyond i.i.d. in the Resource Theory of Asymmetry: An Information-Spectrum Approach for Quantum Fisher Information
• Asymptotic Convertibility of Entanglement: A General Approach to Entanglement Concentration and Dilution
• Stochastic behavior of outcome of Schur-Weyl duality measurement
• Towards the ultimate limits of quantum channel discrimination and quantum communication
• One-shot rates for entanglement manipulation under non-entangling maps
• Asymmetry activation and its relation to coherence under permutation operation
• Max- Relative Entropy of Entanglement, alias Log Robustness
• The Quantum Relative Entropy as a Rate Function and Information Criteria
• Hypothesis Testing of Mixture Distributions using Compressed Data
• Intersection and union of subspaces with applications to communication over authenticated classical-quantum channels and composite hypothesis testing
• Tight relations and equivalences between smooth relative entropies
• Quantum phase classification via partial tomography-based quantum hypothesis testing
• Opportunistic Detection Rules: Finite and Asymptotic Analysis