Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0010114 · Contemporary Physics

Quantum state discrimination

Anthony Chefles

Published Nov 1, 2000• 485 citations
arXivHTMLPDF

Abstract

There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a quantum system is prepared in a member of a known, finite set of states, and the aim is to guess which one with the minimum probability of error. Error free discrimination is also sometimes possible, if we allow for the possibility of obtaining inconclusive results. If no prior information about the state is provided, then it is impractical to try to determine it exactly, and it must be estimated instead. In addition to reviewing these various strategies, I describe connections between state discrimination, the manipulation of quantum entanglement and quantum cloning. Recent experimental work is also discussed.

DOI
10.1080/00107510010002599

Related papers

Quantum Limited State Discrimination

Stephen Mark Barnett

Quantum theory restricts our ability to determine the state of a physical system. This is true even if we know for certain that it was prepared in one of a known set of possible states. I describe two types of optimal strategy for state discrimination. These are (i) state discrimination with minimum probability of error and (ii) unambiguous or error-free state discrimination.

Fortschritte der Physik•Oct 1, 2001•9 citations

Quantum hypothesis testing and state discrimination

J. Prabhu Tej, Syed Raunaq Ahmed, A. R. Usha Devi +1 more

This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error probability, is discussed. Collective and individual adaptive measurement strategies in testing hypotheses in the multiple copy scenario, with various upper and lower bounds on error probability, are outlined. A brief account on quantum channel discrimination and the role of entangled states in achieving enhanced precision in the task of channel discrimination is given.

arXiv:1803.04944•Mar 13, 2018•5 citations

Quantum Hypothesis Testing and State Discrimination

Prabhu Tej, Syed Raunaq Ahmed, I. Reena +2 more

This lecture notes gives a basic survey of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error probability, is discussed. Collective and individual adaptive measurement strategies in testing hypotheses in the multiple copy scenario, with various upper and lower bounds on error probability, are outlined. A brief account on quantum channel discrimination and the role of entangled states in achieving enhanced precision in the task of channel discrimination is given.

International Journal of Research and Analysis in Science and Engineering•Sep 28, 2021•0 citations

Quantum state discrimination and its applications

Joonwoo Bae, L. C. Kwek

Quantum state discrimination underlies various applications in quantum information processing tasks. It essentially describes the distinguishability of quantum systems in different states, and the general process of extracting classical information from quantum systems. It is also useful in quantum information applications, such as the characterization of mutual information in cryptographic protocols, or as a technique for deriving fundamental theorems on quantum foundations. It has deep connections to physical principles such as relativistic causality. Quantum state discrimination traces a long history of several decades, starting with the early attempts to formalize information processing of physical systems such as optical communication with photons. Nevertheless, in most cases, the problems of finding optimal strategies of quantum state discrimination remain unsolved, and related applications are valid in some limited cases only. The present review aims to provide an overview on quantum state discrimination, covering some recent progress, and addressing applications in some selected areas. This review serves to strengthen the link between results in quantum state discrimination and quantum information applications, by showing the ways in which the fundamental results are exploited in applications and vice versa.

arXiv:1707.02571•Journal of Physics A Mathematical and Theoretical•Jan 30, 2015•318 citations

Structure of minimum-error quantum state discrimination

Joonwoo Bae

Distinguishing different quantum states is a fundamental task having practical applications in information processing. Despite the effort devoted so far, however, strategies for optimal discrimination are known only for specific examples. In this paper we consider the problem of minimum-error quantum state discrimination where one attempts to minimize the average error. We show the general structure of minimum-error state discrimination as well as useful properties to derive analytic solutions. Based on the general structure, we present a geometric formulation of the problem, which can be applied to cases where quantum state geometry is clear. We also introduce equivalent classes of sets of quantum states in terms of minimum-error discrimination: sets of quantum states in an equivalent class that share the same guessing probability. In particular, for qubit states where the state geometry is found with the Bloch sphere, we illustrate that for an arbitrary set of qubit states, the minimum-error state discrimination with equal prior probabilities can be analytically solved, that is, optimal measurement and the guessing probability are explicitly obtained.

arXiv:1210.2845•New Journal of Physics•Jul 18, 2013•81 citations

Quantum-state comparison and discrimination

A. Hayashi, T. Hashimoto, M. Horibe

We investigate the performance of discrimination strategy in the comparison task of known quantum states. In the discrimination strategy, one infers whether or not two quantum systems are in the same state on the basis of the outcomes of separate discrimination measurements on each system. In some cases with more than two possible states, the optimal strategy in minimum-error comparison is that one should infer the two systems are in different states without any measurement, implying that the discrimination strategy performs worse than the trivial ``no-measurement'' strategy. We present a sufficient condition for this phenomenon to happen. For two pure states with equal prior probabilities, we determine the optimal comparison success probability with an error margin, which interpolates the minimum-error and unambiguous comparison. We find that the discrimination strategy is not optimal except for the minimum-error case.

arXiv:1803.09030•Physical Review A•May 21, 2018•3 citations
There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a quantum system is prepared in a member of a known, finite set of states, and the aim is to guess which one with the minimum probability of error. Error free discrimination is also sometimes possible, if we allow for the possibility of obtaining inconclusive results. If no prior information about the state is provided, then it is impractical to try to determine it exactly, and it must be estimated instead. In addition to reviewing these various strategies, I describe connections between state discrimination, the manipulation of quantum entanglement and quantum cloning. Recent experimental work is also discussed.
This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error probability, is discussed. Collective and individual adaptive measurement strategies in testing hypotheses in the multiple copy scenario, with various upper and lower bounds on error probability, are outlined. A brief account on quantum channel discrimination and the role of entangled states in achieving enhanced precision in the task of channel discrimination is given.
This lecture notes gives a basic survey of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error probability, is discussed. Collective and individual adaptive measurement strategies in testing hypotheses in the multiple copy scenario, with various upper and lower bounds on error probability, are outlined. A brief account on quantum channel discrimination and the role of entangled states in achieving enhanced precision in the task of channel discrimination is given.
Quantum state discrimination underlies various applications in quantum information processing tasks. It essentially describes the distinguishability of quantum systems in different states, and the general process of extracting classical information from quantum systems. It is also useful in quantum information applications, such as the characterization of mutual information in cryptographic protocols, or as a technique for deriving fundamental theorems on quantum foundations. It has deep connections to physical principles such as relativistic causality. Quantum state discrimination traces a long history of several decades, starting with the early attempts to formalize information processing of physical systems such as optical communication with photons. Nevertheless, in most cases, the problems of finding optimal strategies of quantum state discrimination remain unsolved, and related applications are valid in some limited cases only. The present review aims to provide an overview on quantum state discrimination, covering some recent progress, and addressing applications in some selected areas. This review serves to strengthen the link between results in quantum state discrimination and quantum information applications, by showing the ways in which the fundamental results are exploited in applications and vice versa.
Distinguishing different quantum states is a fundamental task having practical applications in information processing. Despite the effort devoted so far, however, strategies for optimal discrimination are known only for specific examples. In this paper we consider the problem of minimum-error quantum state discrimination where one attempts to minimize the average error. We show the general structure of minimum-error state discrimination as well as useful properties to derive analytic solutions. Based on the general structure, we present a geometric formulation of the problem, which can be applied to cases where quantum state geometry is clear. We also introduce equivalent classes of sets of quantum states in terms of minimum-error discrimination: sets of quantum states in an equivalent class that share the same guessing probability. In particular, for qubit states where the state geometry is found with the Bloch sphere, we illustrate that for an arbitrary set of qubit states, the minimum-error state discrimination with equal prior probabilities can be analytically solved, that is, optimal measurement and the guessing probability are explicitly obtained.
We investigate the performance of discrimination strategy in the comparison task of known quantum states. In the discrimination strategy, one infers whether or not two quantum systems are in the same state on the basis of the outcomes of separate discrimination measurements on each system. In some cases with more than two possible states, the optimal strategy in minimum-error comparison is that one should infer the two systems are in different states without any measurement, implying that the discrimination strategy performs worse than the trivial ``no-measurement'' strategy. We present a sufficient condition for this phenomenon to happen. For two pure states with equal prior probabilities, we determine the optimal comparison success probability with an error margin, which interpolates the minimum-error and unambiguous comparison. We find that the discrimination strategy is not optimal except for the minimum-error case.