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/0311192

On the meaning of entanglement in quantum measurement

Fedor Herbut

Published Nov 27, 2003• 2 citations
arXivHTMLPDF

Abstract

Measurement interaction between a measured object and a measuring instrument, if both are initially in a pure state, produces a (final) bipartite entangled state vector. The quasi-classical part of the correlations in it is connected with transmission of information in the measurement. But, prior to "reading" the instrument, there is also purely quantum entanglement in the final state vector. It is shown that in repeatable measurement quantitatively the entanglement equals the amount of incompatibility between the measured observable and the final state. It also equals the amount of incompatibility of the observable and the initial state of the object.

DOI
10.48550/arxiv.quant-ph/0311192

Related papers

Classical Correlations and Entanglement in Quantum Measurements

Vlatko Vedral

We analyze a quantum measurement where the apparatus is initially in a mixed state. We show that the amount of information gained in a measurement is not equal to the amount of entanglement between the system and the apparatus, but is instead equal to the degree of classical correlations between the two. As a consequence, we derive an uncertainty-like expression relating the information gain in the measurement and the initial mixedness of the apparatus. Final entanglement between the environment and the apparatus is also shown to be relevant for the efficiency of the measurement.

arXiv:quant-ph/0207116•Physical Review Letters•Feb 3, 2003•289 citations

A quantum measure of coherence and incompatibility

Abstract. The well-known two-slit interference is understood as a special relation between observable (localization at the slits) and state (being on both slits). Relation between an observable and a quantum state is investigated in the general case. It is assumed that the amount of coherence equals that of incompatibility between observable and state. On ground of this, an argument is presented that leads to a natural quantum measure of coherence, called ”coherence or incompatibility information”. Its properties are studied in detail making use of ’the mixing property of relative entropy ’ derived in this article. A precise relation between the measure of coherence of an observable and that of its coarsening is obtained and discussed from the intuitive point of view. Convexity of the measure is proved, and thus the fact that it is an information entity is established. A few more detailed properties of coherence information are derived with a view to investigate final-state entanglement in general repeatable measurement, and, more importantly, general bipartite entanglement in follow ups of this study.

•Jan 1, 2005•0 citations

A quantum measure of coherence and incompatibility

Fedor Herbut

The well-known two-slit interference is understood as a special relation between an observable (localization at the slits) and a state (being on both slits). The relation between an observable and a quantum state is investigated in the general case. It is assumed that the amount of coherence equals that of the incompatibility between an observable and a state. On these grounds, an argument is presented that leads to a natural quantum measure of coherence, called 'coherence or incompatibility information'. Its properties are studied in detail, making use of 'the mixing property of relative entropy' derived in this paper. A precise relation between the measure of coherence of an observable and that of its coarsening is obtained and discussed from the intuitive point of view. Convexity of the measure is proved, and thus the fact that it is an information entity is established. A few more detailed properties of the coherence information are derived with a view to investigating the final-state entanglement in general repeatable measurement, and, more importantly, general bipartite entanglement in follow-ups of this study.

arXiv:quant-ph/0503077•Journal of Physics A Mathematical and General•Mar 15, 2005•34 citations

Chains of quasiclassical information for bipartite correlations and the role of twin observables

Fedor Herbut

Having the quantum correlations in a general mixed or pure bipartite state in mind, the part of information accessible by simultaneous measurement on both subsystems is shown never to exceed the part accessible by measurement on one subsystem, which, in turn is proved not to exceed the von Neumann mutual information. A particular pair of (opposite-subsystem) observables is shown to be responsible both for the amount of quasiclassical correlations and for that of the purely quantum entanglement in the pure-state case: the former via simultaneous subsystem measurements, and the latter through the entropy of coherence or of incompatibility, which is defined for the general case. The observables at issue are so-called twin observables. A general definition of the latter is given in terms of their detailed properties.

arXiv:quant-ph/0305187•Physical Review A•Nov 22, 2002•10 citations

Entanglement preventing measurements on simple quantum systems

Paul Bracken

The nature and role of the measuring apparatus in the process of measurement in quantum mechanics is discussed. In the Schrödinger picture, the measurement generates an entanglement between the eigenstates of the observable and the states of the apparatus, which becomes part of the overall system. It is shown that with respect to some small systems, this entanglement can be prevented, and that it should be possible to carry out such experiments.

Molecular Physics•Aug 10, 2005•0 citations

Measures of entanglement in quantum mechanics

Geir Ove Myhr

I give an overview of some of the most used measures of entanglement. To make the presentation self-contained, a number of concepts from quantum information theory are first explained. Then the structure of bipartite entanglement is studied qualitatively, before a number of bipartite entanglement measures are described, both for pure and mixed states. Results from the study of multipartite systems and continuous variable systems are briefly discussed.

arXiv:quant-ph/0408094•Aug 14, 2004•6 citations
Measurement interaction between a measured object and a measuring instrument, if both are initially in a pure state, produces a (final) bipartite entangled state vector. The quasi-classical part of the correlations in it is connected with transmission of information in the measurement. But, prior to "reading" the instrument, there is also purely quantum entanglement in the final state vector. It is shown that in repeatable measurement quantitatively the entanglement equals the amount of incompatibility between the measured observable and the final state. It also equals the amount of incompatibility of the observable and the initial state of the object.
We analyze a quantum measurement where the apparatus is initially in a mixed state. We show that the amount of information gained in a measurement is not equal to the amount of entanglement between the system and the apparatus, but is instead equal to the degree of classical correlations between the two. As a consequence, we derive an uncertainty-like expression relating the information gain in the measurement and the initial mixedness of the apparatus. Final entanglement between the environment and the apparatus is also shown to be relevant for the efficiency of the measurement.
Abstract. The well-known two-slit interference is understood as a special relation between observable (localization at the slits) and state (being on both slits). Relation between an observable and a quantum state is investigated in the general case. It is assumed that the amount of coherence equals that of incompatibility between observable and state. On ground of this, an argument is presented that leads to a natural quantum measure of coherence, called ”coherence or incompatibility information”. Its properties are studied in detail making use of ’the mixing property of relative entropy ’ derived in this article. A precise relation between the measure of coherence of an observable and that of its coarsening is obtained and discussed from the intuitive point of view. Convexity of the measure is proved, and thus the fact that it is an information entity is established. A few more detailed properties of coherence information are derived with a view to investigate final-state entanglement in general repeatable measurement, and, more importantly, general bipartite entanglement in follow ups of this study.
The well-known two-slit interference is understood as a special relation between an observable (localization at the slits) and a state (being on both slits). The relation between an observable and a quantum state is investigated in the general case. It is assumed that the amount of coherence equals that of the incompatibility between an observable and a state. On these grounds, an argument is presented that leads to a natural quantum measure of coherence, called 'coherence or incompatibility information'. Its properties are studied in detail, making use of 'the mixing property of relative entropy' derived in this paper. A precise relation between the measure of coherence of an observable and that of its coarsening is obtained and discussed from the intuitive point of view. Convexity of the measure is proved, and thus the fact that it is an information entity is established. A few more detailed properties of the coherence information are derived with a view to investigating the final-state entanglement in general repeatable measurement, and, more importantly, general bipartite entanglement in follow-ups of this study.
Having the quantum correlations in a general mixed or pure bipartite state in mind, the part of information accessible by simultaneous measurement on both subsystems is shown never to exceed the part accessible by measurement on one subsystem, which, in turn is proved not to exceed the von Neumann mutual information. A particular pair of (opposite-subsystem) observables is shown to be responsible both for the amount of quasiclassical correlations and for that of the purely quantum entanglement in the pure-state case: the former via simultaneous subsystem measurements, and the latter through the entropy of coherence or of incompatibility, which is defined for the general case. The observables at issue are so-called twin observables. A general definition of the latter is given in terms of their detailed properties.