Lower Bounds on Error Exponents via a New Quantum Decoder

Abstract

We introduce a new quantum decoder based on a variant of the pretty good measurement, but defined via an alternative matrix quotient. We use this decoder to show new lower bounds on the error exponent both in the one-shot and asymptotic regimes for the classical-quantum and the entanglement-assisted channel coding problem. Our bounds are expressed in terms of measured (for the one-shot bounds) and sandwiched (for the asymptotic bounds) channel Rényi mutual information of order between 1/2 and 1. Our results are not comparable with some previously established bounds for general instances, yet they are tight (for rates close to capacity) when the underlying channel is classical.

arXiv commentv2: further properties of the new measurement are discussed

References in corpus (30)

• On quantum Renyi entropies: a new generalization and some properties
• The Quantum Chernoff Bound
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Coding Theorem and Strong Converse for Quantum Channels
• A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
• Sandwiched Rényi Divergence Satisfies Data Processing Inequality
• Monotonicity of a relative Rényi entropy
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
• The ${\chi }^2$-divergence and Mixing times of quantum Markov processes
• Classical data compression with quantum side information
• Universal recovery maps and approximate sufficiency of quantum relative entropy
• Correlation Detection and an Operational Interpretation of the Renyi Mutual Information
• Strong converse exponent for classical-quantum channel coding
• One shot entanglement assisted classical and quantum communication over noisy quantum channels: A hypothesis testing and convex split approach
• Multiplicativity of completely bounded $p$-norms implies a strong converse for entanglement-assisted capacity
• Multivariate Trace Inequalities
• On Variational Expressions for Quantum Relative Entropies
• Lower bounds on the Probability of Error for Classical and Classical-Quantum Channels
• Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels
• On the Second-Order Asymptotics for Entanglement-Assisted Communication
• A limit of the quantum Renyi divergence
• Moderate deviation analysis for classical communication over quantum channels
• Applications of position-based coding to classical communication over quantum channels
• On Composite Quantum Hypothesis Testing
• Non-Asymptotic Classical Data Compression with Quantum Side Information
• Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels
• Convexity of quasi-entropy type functions: Lieb's and Ando's convexity theorems revisited
• Achievable error exponents of data compression with quantum side information and communication over symmetric classical-quantum channels
• Strong Converse Exponent for Entanglement-Assisted Communication

Cited by in corpus (2)

• Tight lower bound on the error exponent of classical-quantum channels
• Reliable Simulation of Quantum Channels: the Error Exponent