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

WORLD SCIENTIFIC eBooks

Density Matrix and the Wigner Distribution Function

Published Feb 19, 2017• 0 citations
Publisher
DOI
10.1142/9789813207929_0015

Related papers

Density Matrix and the Wigner Distribution Function

IMPERIAL COLLEGE PRESS eBooks•Jan 1, 2006•0 citations

Wigner Distributions as Representations of the Density Matrix

Leon W. Cohen

Springer eBooks•Jan 1, 1987•2 citations

Exponential approximation for the density matrix and the Wigner's distribution

Max L. Berkowitz

Chemical Physics Letters•Sep 1, 1986•65 citations

Discrete Wigner distribution for two qubits: a characterization of entanglement properties

Riccardo Franco, Vittorio Penna

We study the properties of the discrete Wigner distribution for two qubits introduced by Wotters. In particular, we analyse the entanglement properties within the Wigner distribution picture by considering the negativity of the Wigner function (WF) and the correlations of the marginal distribution. We show that a state is entangled if at least one among the values assumed by the corresponding discrete WF is smaller than a certain critical (negative) value. Then, based on the partial transposition criterion, we establish a relation between the separability of a density matrix and the non-negativity of the WFs relevant both to such a density matrix and to the partially transposed thereof. Finally, we derive a simple inequality—involving the covariance-matrix elements of a given WF—which appears to provide a separability criterion stronger than the one based on the local uncertainty relations.

arXiv:quant-ph/0509050•Journal of Physics A Mathematical and General•May 3, 2006•16 citations

Working in phase‐space with Wigner and Weyl

J. Ben-Benjamin, Moochan B. Kim, Wolfgang P. Schleich +2 more

Quantum phase‐space distributions offer a royal road into the fascinating quantum–classical interface; the Wigner function being the first and best example. However, the subject is frequent with subtleties and textbook‐level misinformation; e.g. “The Wigner distribution can give wrong answers for some operator expectation values” . Since the Wigner distribution is just another representation of the density matrix, it must yield correct answers. To that end, Marlan Scully has asked at several international conferences (the 2015 Prague conference being one of them) the following question: “Starting with the density matrix (not the Moyal characteristic function), could you give me a simple direct derivation of the Wigner distribution?” Section contains his answer. In Appendix D , we give a related treatment and make contact with other approaches. We hope that as a result of our studies, the Wigner distribution will become more deeply appreciated.

Fortschritte der Physik•Nov 15, 2016•11 citations

The Wigner distribution function

GERALD J. IAFRATE, H. L. Grubin, David K. Ferry

Physics Letters A•Jan 1, 1982•27 citations
We study the properties of the discrete Wigner distribution for two qubits introduced by Wotters. In particular, we analyse the entanglement properties within the Wigner distribution picture by considering the negativity of the Wigner function (WF) and the correlations of the marginal distribution. We show that a state is entangled if at least one among the values assumed by the corresponding discrete WF is smaller than a certain critical (negative) value. Then, based on the partial transposition criterion, we establish a relation between the separability of a density matrix and the non-negativity of the WFs relevant both to such a density matrix and to the partially transposed thereof. Finally, we derive a simple inequality—involving the covariance-matrix elements of a given WF—which appears to provide a separability criterion stronger than the one based on the local uncertainty relations.
Quantum phase‐space distributions offer a royal road into the fascinating quantum–classical interface; the Wigner function being the first and best example. However, the subject is frequent with subtleties and textbook‐level misinformation; e.g. “The Wigner distribution can give wrong answers for some operator expectation values” . Since the Wigner distribution is just another representation of the density matrix, it must yield correct answers. To that end, Marlan Scully has asked at several international conferences (the 2015 Prague conference being one of them) the following question: “Starting with the density matrix (not the Moyal characteristic function), could you give me a simple direct derivation of the Wigner distribution?” Section contains his answer. In Appendix D , we give a related treatment and make contact with other approaches. We hope that as a result of our studies, the Wigner distribution will become more deeply appreciated.