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/0511043

On the Sufficient Optimality Condition for Quantum Information Processing

V. P. Belavkin, A. G. Vantsyan

Published Nov 4, 2005• 0 citations
arXivHTMLPDF

Abstract

The necessary and sufficient conditions of optimality of the decoding of quantum signals minimizing the Bayesian risk are generalized for the Shannon mutual information criteria. It is shown that for a linear channel with Gaussian boson noise these conditions are satisfied by coherent quasi-measurement of the canonical annihilation amplitudes in the received superposition.

DOI
10.48550/arxiv.quant-ph/0511043

Related papers

Optimization of Quantum Information Processing at Mutual Information Criterion

V. P. Belavkin, Rouslan L. Stratonovich

A model of quantum noisy channel with input encoding by a classical random vector is described. An equation of optimality is derived to de-termine a complete set of wave functions describing quantum decodings based on quasi-measurements maximizing the classical amount of trans-mitted information. A solution of this equation is found for the Gaussian multimode case with input Gaussian distribution. It is described by the overcomplete family of coherent vectors describing an optimal quasimea-surement of the canonical annihilation amplitudes in the output Hilbert space. It is found that the optimal decoding in this case realizes the maxi-mum amount I = Sp ln

•Jan 1, 1973•0 citations

Optimization of Quantum Information Processing Maximizing Mutual Information

V. P. Belavkin, Rouslan L. Stratonovich

A model of quantum noisy channel with input encoding by a classical random vector is described. An equation of optimality is derived to determine a complete set of wave functions describing quantum decodings based on quasi-measurements maximizing the classical amount of transmitted information. A solution of this equation is found for the Gaussian multimode case with input Gaussian distribution. It is described by the overcomplete family of coherent vectors describing an optimal quasimeasurement of the canonical annihilation amplitudes in the output Hilbert space. It is found that the optimal decoding in this case realizes the maximum amount I=Spln[1+S/(N+1)] of the classical information as transmitted via the classical Gaussian channel with the effective noise covariance matrix N+I. A physical realization of optimal quasi-measurement based on an indirect (heterodyne) observation of the canonical operators is suggested.

arXiv:quant-ph/0511042•Nov 4, 2005•3 citations

On Maximum Mutual Information without Coding

Masao Osaki, Masashi Ban, Osamu Hirota

We consider the communication systems sending the classical (Shannon) information through the quantum channel. The classical information source X is represented with symbols and their a priori probabilities At a transmitter, each symbol is modulated to a quantum state and detected at a receiver by the quantum mechanically generalized measurement, so-called the probability operator-valued measure Here we call a detection operator since it represents a detection process deciding a received signal to be ‘j’. The detection operator is no-negative, and resolution of identity, where is the identity operator on the signal Hilbert space spanned by signal quantum states. This detection process can be regarded as a quantum channel characterized by the conditional probability defined as follows:

Kluwer Academic Publishers eBooks•Dec 19, 2005•2 citations

Quantum mechanical linear filtering of vector signal processes

John S. Baras, Robert O. Harger

The problem of estimating a member of a discrete-time vector process from past and present quantum mechanical measurements is considered; specifically, the minimum-variance linear estimator based on optimal present measurements is studied. Necessary and sufficient conditions that characterize the optimal processing matrix coefficients and the optimal measurements are discussed and interpreted. The optimal linear filter is compared to the optimal quantum estimator without postprocessing of past data. When the signal sequence is pairwise Gaussian and the optimal quantum measurement without postproccssing has the properties that it is linear in a specific sense and that its outcome and the corresponding element of the signal sequence are jointly Gaussian, then the optimal linear filter separates. That is, the optimal measurement can be taken to be the same as thc optimal measurement without regard to past data, and the past and present data are processed classically. Thc results are illustrated by considering the filtering of the in-phase and quadrature amplitudes of a laser field received in a single-mode cavity along with thermal noise. In this case, when the random signal sequence satisfies a linear recursion, the estimate can be computed recursively in a very efficient manner.

IEEE Transactions on Information Theory•Nov 1, 1977•11 citations

The maximum mutual information without coding for binary quantum-state signals

Masao Osaki, Osamu Hirota, Masashi Ban

The maximum mutual information without coding is investigated for binary quantum-state signals. The necessary condition for detection operators to represent the information optimal detection is satisfied for M-ary symmetric quantum-state signals by the detection operators derived from the quantum minimax strategy while its purpose is a minimization of the error probability. The true maximum mutual information is numerically analysed for the binary case.

Journal of Modern Optics•Feb 1, 1998•19 citations

The quantum generalization of optimal statistical estimation and hypothesis testing

Rouslan L. Stratonovich

A review of the fundamental ideas and methods of the optimal reception and processing of quantum signals is given. Estimation via an operator based on the usual and generalized measurements (e.g., quasi-measurements) are discussed. The theory of operator estimation enables one to obtain Bayes limits for the usual estimates. The change from usual measurements to quasi-measurements generally improves performance. We show that some quasi-measurements can be realized as indirect measurements, and introduce an operator measure II(db) which describes the quasi-measurements on the space of measurements. Estimation based on quasi-measurements is described by operator measures Q(du) on the space of estimates. Minimization with respect to Q(du) is minimization simultaneously for all quasi-measurements and all estimates. For the M-ary hypothesis testing problem finding the optimum reduces to finding non-negative definite Hermitian operators Q1,…, Q m satisfying Q1+…+Q m = 1 where 1 is the identity operator, which extremize. Optimal Bayes quantum estimation is discussed. In the case of Gaussian quantum signal and minimum variance estimation, finding the quasi-measurements leads to optimal linear estimation. Further suboptimal methods for finding the operator in more general cases are discussed.

Stochastics•Jan 1, 1973•17 citations
The necessary and sufficient conditions of optimality of the decoding of quantum signals minimizing the Bayesian risk are generalized for the Shannon mutual information criteria. It is shown that for a linear channel with Gaussian boson noise these conditions are satisfied by coherent quasi-measurement of the canonical annihilation amplitudes in the received superposition.
A model of quantum noisy channel with input encoding by a classical random vector is described. An equation of optimality is derived to de-termine a complete set of wave functions describing quantum decodings based on quasi-measurements maximizing the classical amount of trans-mitted information. A solution of this equation is found for the Gaussian multimode case with input Gaussian distribution. It is described by the overcomplete family of coherent vectors describing an optimal quasimea-surement of the canonical annihilation amplitudes in the output Hilbert space. It is found that the optimal decoding in this case realizes the maxi-mum amount I = Sp ln
A model of quantum noisy channel with input encoding by a classical random vector is described. An equation of optimality is derived to determine a complete set of wave functions describing quantum decodings based on quasi-measurements maximizing the classical amount of transmitted information. A solution of this equation is found for the Gaussian multimode case with input Gaussian distribution. It is described by the overcomplete family of coherent vectors describing an optimal quasimeasurement of the canonical annihilation amplitudes in the output Hilbert space. It is found that the optimal decoding in this case realizes the maximum amount I=Spln[1+S/(N+1)] of the classical information as transmitted via the classical Gaussian channel with the effective noise covariance matrix N+I. A physical realization of optimal quasi-measurement based on an indirect (heterodyne) observation of the canonical operators is suggested.
We consider the communication systems sending the classical (Shannon) information through the quantum channel. The classical information source X is represented with symbols and their a priori probabilities At a transmitter, each symbol is modulated to a quantum state and detected at a receiver by the quantum mechanically generalized measurement, so-called the probability operator-valued measure Here we call a detection operator since it represents a detection process deciding a received signal to be ‘j’. The detection operator is no-negative, and resolution of identity, where is the identity operator on the signal Hilbert space spanned by signal quantum states. This detection process can be regarded as a quantum channel characterized by the conditional probability defined as follows:
The problem of estimating a member of a discrete-time vector process from past and present quantum mechanical measurements is considered; specifically, the minimum-variance linear estimator based on optimal present measurements is studied. Necessary and sufficient conditions that characterize the optimal processing matrix coefficients and the optimal measurements are discussed and interpreted. The optimal linear filter is compared to the optimal quantum estimator without postprocessing of past data. When the signal sequence is pairwise Gaussian and the optimal quantum measurement without postproccssing has the properties that it is linear in a specific sense and that its outcome and the corresponding element of the signal sequence are jointly Gaussian, then the optimal linear filter separates. That is, the optimal measurement can be taken to be the same as thc optimal measurement without regard to past data, and the past and present data are processed classically. Thc results are illustrated by considering the filtering of the in-phase and quadrature amplitudes of a laser field received in a single-mode cavity along with thermal noise. In this case, when the random signal sequence satisfies a linear recursion, the estimate can be computed recursively in a very efficient manner.
A review of the fundamental ideas and methods of the optimal reception and processing of quantum signals is given. Estimation via an operator based on the usual and generalized measurements (e.g., quasi-measurements) are discussed. The theory of operator estimation enables one to obtain Bayes limits for the usual estimates. The change from usual measurements to quasi-measurements generally improves performance. We show that some quasi-measurements can be realized as indirect measurements, and introduce an operator measure II(db) which describes the quasi-measurements on the space of measurements. Estimation based on quasi-measurements is described by operator measures Q(du) on the space of estimates. Minimization with respect to Q(du) is minimization simultaneously for all quasi-measurements and all estimates. For the M-ary hypothesis testing problem finding the optimum reduces to finding non-negative definite Hermitian operators Q1,…, Q m satisfying Q1+…+Q m = 1 where 1 is the identity operator, which extremize. Optimal Bayes quantum estimation is discussed. In the case of Gaussian quantum signal and minimum variance estimation, finding the quasi-measurements leads to optimal linear estimation. Further suboptimal methods for finding the operator in more general cases are discussed.