Entanglement and symmetry in permutation-symmetric states
Abstract
We investigate the relationship between multipartite entanglement and symmetry, focusing on permutation symmetric states. We give a highly intuitive geometric interpretation to entanglement via the Majorana representation, where these states correspond to points on a unit sphere. We use this to show how various entanglement properties are determined by the symmetry properties of the states. The geometric measure of entanglement is thus phrased entirely as a geometric optimization and a condition for the equivalence of entanglement measures written in terms of point symmetries. Finally, we see that different symmetries of the states correspond to different types of entanglement with respect to interconvertibility under stochastic local operations and classical communication.
- Authors:
-
- CNRS, LTCI, Telecom ParisTech, 37/39 rue Dareau, 75014 Paris (France)
- Publication Date:
- OSTI Identifier:
- 21544599
- Resource Type:
- Journal Article
- Journal Name:
- Physical Review. A
- Additional Journal Information:
- Journal Volume: 83; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.83.042332; (c) 2011 American Institute of Physics; Journal ID: ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMMUNICATIONS; GEOMETRY; OPTIMIZATION; QUANTUM ENTANGLEMENT; SPHERES; STOCHASTIC PROCESSES; SYMMETRY; MATHEMATICS
Citation Formats
Markham, Damian J. H. Entanglement and symmetry in permutation-symmetric states. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.83.042332.
Markham, Damian J. H. Entanglement and symmetry in permutation-symmetric states. United States. https://doi.org/10.1103/PHYSREVA.83.042332
Markham, Damian J. H. 2011.
"Entanglement and symmetry in permutation-symmetric states". United States. https://doi.org/10.1103/PHYSREVA.83.042332.
@article{osti_21544599,
title = {Entanglement and symmetry in permutation-symmetric states},
author = {Markham, Damian J. H.},
abstractNote = {We investigate the relationship between multipartite entanglement and symmetry, focusing on permutation symmetric states. We give a highly intuitive geometric interpretation to entanglement via the Majorana representation, where these states correspond to points on a unit sphere. We use this to show how various entanglement properties are determined by the symmetry properties of the states. The geometric measure of entanglement is thus phrased entirely as a geometric optimization and a condition for the equivalence of entanglement measures written in terms of point symmetries. Finally, we see that different symmetries of the states correspond to different types of entanglement with respect to interconvertibility under stochastic local operations and classical communication.},
doi = {10.1103/PHYSREVA.83.042332},
url = {https://www.osti.gov/biblio/21544599},
journal = {Physical Review. A},
issn = {1050-2947},
number = 4,
volume = 83,
place = {United States},
year = {Fri Apr 15 00:00:00 EDT 2011},
month = {Fri Apr 15 00:00:00 EDT 2011}
}