Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination
type: Item
instance of: scholarly article
title: Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination
zbMATH Open document ID: 1309.81042
DOI: 10.1063/1.4898559
author: Koenraad M. R. Audenaert
author: Milán Mosonyi
published in: Journal of Mathematical Physics
publication date: 2014-11-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/1401.7658
full work available at URL: https://biblio.ugent.be/publication/5986925
Mathematics Subject Classification ID: 81P45
Mathematics Subject Classification ID: 81P50
Mathematics Subject Classification ID: 94B70
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 6366331
zbMATH Keywords: quantum-error-deformation
MaRDI profile type: Publication
OpenAlex ID: W2127843284
arXiv ID: 1401.7658
cites work: Q4283112
cites work: Problems of infimum in the positive cone
cites work: Asymptotic error rates in quantum hypothesis testing
cites work: Reversing quantum dynamics with near-optimal quantum and classical fidelity
cites work: An ergodic theorem for the quantum relative entropy
cites work: Min- and Max-Relative Entropies and a New Entanglement Monotone
cites work: Designing optimal quantum detectors via semidefinite programming
cites work: Cryptographic distinguishability measures for quantum-mechanical states
cites work: A ‘Pretty Good’ Measurement for Distinguishing Quantum States
cites work: Quantum detection and estimation theory
cites work: Large deviations and Chernoff bound for certain correlated states on a spin chain
cites work: Error exponents in hypothesis testing for correlated states on a spin chain
cites work: Quantum hypothesis testing with group symmetry
cites work: On Asymptotically Optimal Hypothesis Testing in Quantum Statistics
cites work: The Operational Meaning of Min- and Max-Entropy
cites work: Asymptotic distinguishability measures for shift-invariant quasifree states of fermionic lattice systems
cites work: Block-circulant matrices with circulant blocks, Weil sums, and mutually unbiased bases. II. The prime power case
cites work: Generalized relative entropies and the capacity of classical-quantum channels
cites work: On the Quantum Rényi Relative Entropies and Related Capacity Formulas
cites work: Q2706552
cites work: The Chernoff lower bound for symmetric quantum hypothesis testing
cites work: Exponential error rates in multiple state discrimination on a quantum spin chain
cites work: Asymptotically Optimal Discrimination between Pure Quantum States
cites work: An asymptotic error bound for testing multiple quantum hypotheses
cites work: On Error Exponents in Quantum Hypothesis Testing
cites work: Optimal Sequences of Tests for Several Polynomial Schemes of Trials
cites work: Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo–Curlander bounds
cites work: Two-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on maximum overlap using directional iterates
cites work: Semidefinite Programming
cites work: Optimum testing of multiple hypotheses in quantum detection theory
Recommended article: Exponential error rates in multiple state discrimination on a quantum spin chain
Recommended article: An asymptotic error bound for testing multiple quantum hypotheses
Recommended article: Asymptotic correctability of Bell-diagonal quantum states and maximum tolerable bit-error rates
Recommended article: On the Error Exponents of Binary State Discrimination With Composite Hypotheses
Recommended article: Asymptotic error rates in quantum hypothesis testing
Recommended article: Asymptotically Optimal Discrimination between Pure Quantum States
Recommended article: Bounded-Error Quantum State Identification and Exponential Separations in Communication Complexity
Recommended article: Bounded-error quantum state identification and exponential separations in communication complexity
Recommended article: On Error Exponents in Quantum Hypothesis Testing
Recommended article: Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo–Curlander bounds
review text: In this 39-page multi-mathematical paper the authors have considered in a communicative scenario the multiple hypothesis testing problem for symmetric quantum state discrimination between \(r\) distinct states. After a detailed introduction a summary of the necessary preliminaries and review of many known related results are given in the second section. In the third section the upper bounds from suboptimal measurements are discussed while the fourth section deals with binary state discrimination problem with the fifth section treating in detail the dichotomic discrimination questions. Nussbaum's mixed exponents approach is discussed next whereas the final seventh section is devoted to asymptotics: The Chernoff bound.NEWLINENEWLINE There are 42 references, 5 appendices (with 25 equations) which are quite explanatory, 78 main equations, 14 theorems with proof, 6 conjectures, 9 remarks, 8 lemmas, 1 proposition and 2 corollaries in all.NEWLINENEWLINE Studies in probabilistic approaches and behaviour of anything and everything in nature are extremely important. The paper under review is an eloquent example of this fact.NEWLINENEWLINE Altogether the results are quite interesting and useful.
description: scientific article; zbMATH DE number 6366331