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

Physical Review A

Bound on measurement based on the no-signaling condition

Stephen Mark Barnett, Erika Andersson

Published Apr 10, 2002• 32 citations
Publisher

Abstract

We obtain a tight bound on the measurement which discriminates without error between two nonorthogonal states. The derivation is based on the no-signaling condition, without any reference to generalized measurements.
DOI
10.1103/physreva.65.044307

Related papers

Optimality of minimum-error discrimination by the no-signaling condition

Joonwoo Bae, Jae Weon Lee, Jaewan Kim +1 more

In this work we relate the well-known no-go theorem that two nonorthogonal (mixed) quantum states cannot be perfectly discriminated, to the general principle in physics, the no-signaling condition. In fact, the minimum error in discrimination between two quantum states is derived from the no-signaling condition.

arXiv:0711.0664•Physical Review A•Aug 26, 2008•13 citations

Enhanced quantum state discrimination under general measurements with entanglement and nonorthogonality restrictions

Swati Choudhary, Aparajita Bhattacharyya, Ujjwal Sen

The minimum error probability for distinguishing between two quantum states is bounded by the Helstrom limit, derived under the assumption that measurement strategies are restricted to positive operator-valued measurements. We explore scenarios in which the error probability for discriminating two quantum states can be reduced below the Helstrom bound under some constrained access of resources, indicating the use of measurement operations that go beyond the standard positive operator-valued measurements framework. We refer to such measurements as non-positive operator-valued measurements. While existing literature often associates these measurements with initial entanglement between the system and an auxiliary, followed by joint projective measurement and discarding the auxiliary, we demonstrate that initial entanglement between system and auxiliary is not necessary for the emergence of such measurements in the context of state discrimination. Interestingly, even initial product states can give rise to effective non-positive measurements on the subsystem, and achieve sub-Helstrom discrimination error when discriminating quantum states of the subsystem.

quant-pharXiv:2601.19820•Jan 28, 2026•0 citations

An entropy inequality for quantum measurements

Göran Lindblad

Communications in Mathematical Physics•Sep 1, 1972•66 citations

Noncommutative analogues of the Cramér-Rao inequality in the quantum measurement theory

Alexander Semenovich Holevo

Lecture notes in mathematics•Jan 1, 1976•10 citations

Further Results on the Observability of Quantum Systems Under General Measurement

Domenico D’Alessandro, Raffaele Romano

Quantum Information Processing•May 9, 2006•7 citations

Optimal bounded-error strategies for projective measurements in nonorthogonal-state discrimination

Maximilian Puelma Touzel, Robert B. A. Adamson, Aephraim M. Steinberg

Research in nonorthogonal-state discrimination has given rise to two conventional optimal strategies: unambiguous discrimination (UD) and minimum error discrimination. We explore the experimentally relevant range of measurement strategies between the two, where the rate of inconclusive results is minimized for a bounded-error rate. We first provide some constraints on the problem that apply to generalized measurements [positive-operator-valued measurements (POVMs)]. We then provide the theory for the optimal projective measurement in this range. Through analytical and numerical results we investigate this family of projective, bounded-error strategies and compare it to the POVM family as well as to experimental implementation of UD using POVMs. We also discuss a possible application of these bounded-error strategies to quantum key distribution.

arXiv:0708.1540•Physical Review A•Dec 19, 2007•39 citations
The minimum error probability for distinguishing between two quantum states is bounded by the Helstrom limit, derived under the assumption that measurement strategies are restricted to positive operator-valued measurements. We explore scenarios in which the error probability for discriminating two quantum states can be reduced below the Helstrom bound under some constrained access of resources, indicating the use of measurement operations that go beyond the standard positive operator-valued measurements framework. We refer to such measurements as non-positive operator-valued measurements. While existing literature often associates these measurements with initial entanglement between the system and an auxiliary, followed by joint projective measurement and discarding the auxiliary, we demonstrate that initial entanglement between system and auxiliary is not necessary for the emergence of such measurements in the context of state discrimination. Interestingly, even initial product states can give rise to effective non-positive measurements on the subsystem, and achieve sub-Helstrom discrimination error when discriminating quantum states of the subsystem.
Research in nonorthogonal-state discrimination has given rise to two conventional optimal strategies: unambiguous discrimination (UD) and minimum error discrimination. We explore the experimentally relevant range of measurement strategies between the two, where the rate of inconclusive results is minimized for a bounded-error rate. We first provide some constraints on the problem that apply to generalized measurements [positive-operator-valued measurements (POVMs)]. We then provide the theory for the optimal projective measurement in this range. Through analytical and numerical results we investigate this family of projective, bounded-error strategies and compare it to the POVM family as well as to experimental implementation of UD using POVMs. We also discuss a possible application of these bounded-error strategies to quantum key distribution.