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:1011.0150 · Physical Review A

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

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

Published Dec 20, 2010• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.82.062318

Related papers

Optimal Quantum State Estimation by No-Signaling Principle

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

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.

•Oct 31, 2010•0 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

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 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

Amount of information obtained by a quantum measurement

Serge Massar, Sandu Popescu

In this paper we address the problem of how much can be learned about an unknown quantum state by a measurement. To this end we consider optimal measurements for the state estimation problem, that is measurements that maximize the expectation of a fidelity function. We then enlarge the class of optimal measurements to measurements that act collectively on blocks of input states, and in addition we only require that the fidelity of the measurement be arbitrarily close to the optimal fidelity. We then consider the Shannon information of the outputs of optimal measurements, which is the amount of data produced by the measurements. We show that in the enlarged class of optimal measurements described above one can always construct an optimal measurement so that the Shannon information of its outputs equals the von Neumann entropy of the unknown states. Since this result is valid for all choices of fidelity functions and all distributions of input states, it provides a model independent answer to the question of how much can be learned about a quantum state by a measurement. Namely, this result shows that a measurement can extract at most one meaningful bit from every qubit carried by the unknown state.

arXiv:quant-ph/9907066•Physical Review A•May 12, 2000•30 citations

No-signaling bounds for quantum cloning and metrology

Pavel Sekatski, Michalis Skotiniotis, Wolfgang Dür

The impossibility of superluminal communication is a fundamental principle of physics. Here we show that this principle underpins the performance of several fundamental tasks in quantum information processing and quantum metrology. In particular, we derive tight no-signaling bounds for probabilistic cloning and super-replication that coincide with the corresponding optimal achievable fidelities and rates known. In the context of quantum metrology, we derive the Heisenberg limit from the no-signaling principle for certain scenarios including reference frame alignment and maximum likelihood state estimation. We elaborate on the equivalence of assymptotic phase-covariant cloning and phase estimation for different figures of merit.

arXiv:1412.3361•Physical Review A•Aug 28, 2015•6 citations
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.
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.
In this paper we address the problem of how much can be learned about an unknown quantum state by a measurement. To this end we consider optimal measurements for the state estimation problem, that is measurements that maximize the expectation of a fidelity function. We then enlarge the class of optimal measurements to measurements that act collectively on blocks of input states, and in addition we only require that the fidelity of the measurement be arbitrarily close to the optimal fidelity. We then consider the Shannon information of the outputs of optimal measurements, which is the amount of data produced by the measurements. We show that in the enlarged class of optimal measurements described above one can always construct an optimal measurement so that the Shannon information of its outputs equals the von Neumann entropy of the unknown states. Since this result is valid for all choices of fidelity functions and all distributions of input states, it provides a model independent answer to the question of how much can be learned about a quantum state by a measurement. Namely, this result shows that a measurement can extract at most one meaningful bit from every qubit carried by the unknown state.
The impossibility of superluminal communication is a fundamental principle of physics. Here we show that this principle underpins the performance of several fundamental tasks in quantum information processing and quantum metrology. In particular, we derive tight no-signaling bounds for probabilistic cloning and super-replication that coincide with the corresponding optimal achievable fidelities and rates known. In the context of quantum metrology, we derive the Heisenberg limit from the no-signaling principle for certain scenarios including reference frame alignment and maximum likelihood state estimation. We elaborate on the equivalence of assymptotic phase-covariant cloning and phase estimation for different figures of merit.