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/0601061

Quantum interference and Bayes theorem

Filippo Neri

Published Jan 10, 2006• 0 citations
arXivHTMLPDF

Abstract

This note is a comment on the "quantum interferometry" section of Reference [1]. It points out that the methods of that section can be applied to more general states than the ones that are discussed in Ref. [1].
DOI
10.48550/arxiv.quant-ph/0601061

Related papers

Is Bayes Theorem Applicable to all Quantum States?

H. Razmi, J. Allahyari

arXiv:1407.6618•Iranian Journal of Science and Technology Transactions A Science•Sep 1, 2017•0 citations

Quantum Bayesian methods and subsequent measurements

Filippo Neri

The use of Bayes theorem in quantum mechanics is discussed. It is shown that the quantum Bayes theorem follows from the ordinary quantum measurement theory, when applied to density operators that represent our knowledge of a system. The examples studied involve measurements on multiple copies of the same (unknown) state. The theorem is used to determine the unknown state by successive measurements on several of the copies of the state. An idealized information-theoretic description of propagating CW laser beams is treated in detail. It is shown how photon detections on part of the beams can be used to determine the phase of the rest of the beams. Also discussed, are the limitations on the accuracy of the phase determination that follow from the fact that it is accomplished by the detection of a finite number of photons. Explicit expressions are derived for the conditional probabilities of detecting photons at different locations, given the numbers of photons detected in the past. The quantitative predictions could be used, in principle, to test proposed quantum states of propagating laser beams.

arXiv:quant-ph/0508012•Physical Review A•Dec 6, 2005•8 citations

Some methods for resolution of quantum signals in the presence of Gaussian interference

A. G. Vantsian

Radio Engineering and Electronic Physics•Jan 1, 1977•2 citations

Bayesian Probability in Quantum Mechanics

Rüdiger Schack

Abstract This paper reviews arguments for the claim that all probabilities arising in quantum mechanics are Bayesian degrees of belief. The starting point is the observation that there is a one-to-one map from quantum states to points on the probability simplex. Bayes’s rule remains valid in quantum theory, provided it is kept in mind that the outcomes of quantum measurements have no preassigned values. The probabilities of quantum measurement outcomes depend explicitly on a quantum prior whose general form will be discussed. Similar to the classical case, the quantum de Finetti theorem simplifies the analysis of repeated quantum trials if the prior is exchangeable. The Bayesian approach to quantum theory described here solves the problem of the ‘collapse of the wave function’. It also provides almost trivial explanations of a number of phenomena in quantum information theory, including the no-cloning theorem and quantum teleportation.

•Jul 19, 2007•2 citations

Quantum State Reduction and the Quantum Bayes Principle

Masanao Ozawa

arXiv:quant-ph/9705030•Springer eBooks•Jan 1, 1997•18 citations

Entanglement purification of unknown quantum states

Todd A. Brun, Carlton M. Caves, Rüdiger Schack

A concern has been expressed that ``the Jaynes principle can produce fake entanglement'' [R. Horodecki et al., Phys. Rev. A 59, 1799 (1999)]. In this paper we discuss the general problem of distilling maximally entangled states from N copies of a bipartite quantum system about which only partial information is known, for instance, in the form of a given expectation value. We point out that there is indeed a problem with applying the Jaynes principle of maximum entropy to more than one copy of a system, but the nature of this problem is classical and was discussed extensively by Jaynes. Under the additional assumption that the state ${\ensuremath{\rho}}^{(N)}$ of the N copies of the quantum system is exchangeable, one can write down a simple general expression for ${\ensuremath{\rho}}^{(N)}.$ By measuring one or more of the subsystems, one can gain information and update the state estimate for the remaining subsystems with the quantum version of the Bayes rule. Using this rule, we show how to modify two standard entanglement purification protocols, one-way hashing and recurrence, so that they can be applied to exchangeable states. We thus give an explicit algorithm for distilling entanglement from an unknown or partially known quantum state.

arXiv:quant-ph/0010038•Physical Review A•Mar 21, 2001•27 citations
The use of Bayes theorem in quantum mechanics is discussed. It is shown that the quantum Bayes theorem follows from the ordinary quantum measurement theory, when applied to density operators that represent our knowledge of a system. The examples studied involve measurements on multiple copies of the same (unknown) state. The theorem is used to determine the unknown state by successive measurements on several of the copies of the state. An idealized information-theoretic description of propagating CW laser beams is treated in detail. It is shown how photon detections on part of the beams can be used to determine the phase of the rest of the beams. Also discussed, are the limitations on the accuracy of the phase determination that follow from the fact that it is accomplished by the detection of a finite number of photons. Explicit expressions are derived for the conditional probabilities of detecting photons at different locations, given the numbers of photons detected in the past. The quantitative predictions could be used, in principle, to test proposed quantum states of propagating laser beams.
Abstract This paper reviews arguments for the claim that all probabilities arising in quantum mechanics are Bayesian degrees of belief. The starting point is the observation that there is a one-to-one map from quantum states to points on the probability simplex. Bayes’s rule remains valid in quantum theory, provided it is kept in mind that the outcomes of quantum measurements have no preassigned values. The probabilities of quantum measurement outcomes depend explicitly on a quantum prior whose general form will be discussed. Similar to the classical case, the quantum de Finetti theorem simplifies the analysis of repeated quantum trials if the prior is exchangeable. The Bayesian approach to quantum theory described here solves the problem of the ‘collapse of the wave function’. It also provides almost trivial explanations of a number of phenomena in quantum information theory, including the no-cloning theorem and quantum teleportation.
A concern has been expressed that ``the Jaynes principle can produce fake entanglement'' [R. Horodecki et al., Phys. Rev. A 59, 1799 (1999)]. In this paper we discuss the general problem of distilling maximally entangled states from N copies of a bipartite quantum system about which only partial information is known, for instance, in the form of a given expectation value. We point out that there is indeed a problem with applying the Jaynes principle of maximum entropy to more than one copy of a system, but the nature of this problem is classical and was discussed extensively by Jaynes. Under the additional assumption that the state ${\ensuremath{\rho}}^{(N)}$ of the N copies of the quantum system is exchangeable, one can write down a simple general expression for ${\ensuremath{\rho}}^{(N)}.$ By measuring one or more of the subsystems, one can gain information and update the state estimate for the remaining subsystems with the quantum version of the Bayes rule. Using this rule, we show how to modify two standard entanglement purification protocols, one-way hashing and recurrence, so that they can be applied to exchangeable states. We thus give an explicit algorithm for distilling entanglement from an unknown or partially known quantum state.