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

Optimal Quantum State Estimation by No-Signaling Principle

Yeong Deok Han, Joonwoo Bae, Xiang‐Bin Wang, Won-Young Hwang

Published Oct 31, 2010• 0 citations
OpenAlex

Abstract

We obtain a simple derivation of the optimal quantum state estimation of a two-level system using the no-signaling principle. In particular, we show that the no-signaling principle determines the unique form of the guessing probability, independently to a given figure of merit such as the fidelity or the information gain. This proves that optimal measurements for a two-level quantum system is the same for almost all figures of merit.

Related papers

Optimal quantum state estimation with use of the no-signaling principle

Yeong Deok Han, Joonwoo Bae, Xiang‐Bin Wang +1 more

A simple derivation of the optimal state estimation of a quantum bit was obtained by using the no-signaling principle. In particular, the no-signaling principle determines a unique form of the guessing probability independent of figures of merit, such as the fidelity or information gain. This proves that the optimal estimation for a quantum bit can be achieved by the same measurement for almost all figures of merit.

arXiv:1011.0150•Physical Review A•Dec 20, 2010•4 citations

No-Signaling Principle Can Determine Optimal Quantum State Discrimination

Joonwoo Bae, Won-Young Hwang, Yeong Deok Han

We provide a general framework of utilizing the no-signaling principle in derivation of the guessing probability in the minimum-error quantum state discrimination. We show that, remarkably, the guessing probability can be determined by the no-signaling principle. This is shown by proving that, in the semidefinite programing for the discrimination, the optimality condition corresponds to the constraint that quantum theory cannot be used for a superluminal communication. Finally, a general bound to the guessing probability is presented in a closed form.

arXiv:1102.0361•Physical Review Letters•Oct 20, 2011•38 citations

Quantum state discrimination with general figures of merit

Won-Young Hwang, Yeong Deok Han

We solve the problem of quantum state discrimination with ``general (symmetric) figures of merit'' for an even number of symmetric quantum bits with use of the no-signaling principle. It turns out that conditional probability has the same form for any figure of merit. Optimal measurement and corresponding conditional probability are the same for any monotonous figure of merit.

arXiv:1208.5378•Physical Review A•Sep 27, 2012•0 citations

Quantum State Reconstruction From Incomplete Data

Vladimír Bužek, G. Drobný, R. Derka +2 more

Knowing and guessing, these are two essential epistemological pillars in the theory of quantum-mechanical measurement. As formulated quantum mechanics is a statistical theory. In general, a priori unknown states can be completely determined only when measurements on infinite ensembles of identically prepared quantum systems are performed. But how one can estimate (guess) quantum state when just incomplete data are available (known)? What is the most reliable estimation based on a given measured data? What is the optimal measurement providing only a finite number of identically prepared quantum objects are available? These are some of the questions we address. We present several schemes for a reconstruction of states of quantum systems from measured data: (1) We show how the maximum entropy (MaxEnt) principle can be efficiently used for an estimation of quantum states on incomplete observation levels. (2) We show how Bayesian inference can be used for reconstruction of quantum states when only a finite number of identically prepared systems are measured. (3) We describe the optimal generalized measurement of a finite number of identically prepared quantum systems which results in the estimation of a quantum state with the highest fidelity.

arXiv:quant-ph/9805020•May 7, 1998•22 citations

Asymptotic performance of optimal state estimation in quantum two level system

Masahito Hayashi, Keiji Matsumoto

We derived an asymptotic bound the accuracy of the estimation when we use the quantum correlation in the measuring apparatus. It is also proved that this bound can be achieved in any model in the quantum two-level system. Moreover, we show that this bound of such a model cannot be attained by any quantum measurement with no quantum correlation in the measuring apparatus. That is, in such a model, the quantum correlation can improve the accuracy of the estimation in an asymptotic setting.

arXiv:quant-ph/0411073•Nov 10, 2004•21 citations

No-signaling bound on quantum state discrimination

Sarah Croke, Erika Andersson, Stephen Mark Barnett

Quantum correlations do not allow signaling, and any operation which may be performed on one system of an entangled pair cannot be detected by measurement of the other system alone. This no-signaling condition limits allowed operations and, in the context of quantum communication, may be used to put bounds on quantum state discrimination. We find that the natural figure of merit to consider is the confidence in identifying a state, which is optimized by the maximum confidence strategy. We show that this strategy may be derived from the no-signaling condition, and demonstrate the relationship between maximum confidence measurements and entanglement concentration.

arXiv:0708.3909•Physical Review A•Jan 28, 2008•27 citations
We obtain a simple derivation of the optimal quantum state estimation of a two-level system using the no-signaling principle. In particular, we show that the no-signaling principle determines the unique form of the guessing probability, independently to a given figure of merit such as the fidelity or the information gain. This proves that optimal measurements for a two-level quantum system is the same for almost all figures of merit.
We provide a general framework of utilizing the no-signaling principle in derivation of the guessing probability in the minimum-error quantum state discrimination. We show that, remarkably, the guessing probability can be determined by the no-signaling principle. This is shown by proving that, in the semidefinite programing for the discrimination, the optimality condition corresponds to the constraint that quantum theory cannot be used for a superluminal communication. Finally, a general bound to the guessing probability is presented in a closed form.
Knowing and guessing, these are two essential epistemological pillars in the theory of quantum-mechanical measurement. As formulated quantum mechanics is a statistical theory. In general, a priori unknown states can be completely determined only when measurements on infinite ensembles of identically prepared quantum systems are performed. But how one can estimate (guess) quantum state when just incomplete data are available (known)? What is the most reliable estimation based on a given measured data? What is the optimal measurement providing only a finite number of identically prepared quantum objects are available? These are some of the questions we address. We present several schemes for a reconstruction of states of quantum systems from measured data: (1) We show how the maximum entropy (MaxEnt) principle can be efficiently used for an estimation of quantum states on incomplete observation levels. (2) We show how Bayesian inference can be used for reconstruction of quantum states when only a finite number of identically prepared systems are measured. (3) We describe the optimal generalized measurement of a finite number of identically prepared quantum systems which results in the estimation of a quantum state with the highest fidelity.
Quantum correlations do not allow signaling, and any operation which may be performed on one system of an entangled pair cannot be detected by measurement of the other system alone. This no-signaling condition limits allowed operations and, in the context of quantum communication, may be used to put bounds on quantum state discrimination. We find that the natural figure of merit to consider is the confidence in identifying a state, which is optimized by the maximum confidence strategy. We show that this strategy may be derived from the no-signaling condition, and demonstrate the relationship between maximum confidence measurements and entanglement concentration.