The University of Southampton
University of Southampton Institutional Repository

The mixed two-qubit system and the structure of its ring of local invariants

The mixed two-qubit system and the structure of its ring of local invariants
The mixed two-qubit system and the structure of its ring of local invariants
The local invariants of a mixed two-qubit system are discussed. These invariants are polynomials in the elements of the corresponding density matrix. They are counted by means of group-theoretic branching rules which relate this problem to one arising in spin-isospin nuclear shell models. The corresponding Molien series and a refinement in the form of a 4-parameter generating function are determined. A graphical approach is then used to construct explicitly a fundamental set of 21 invariants. Relations between them are found in the form of syzygies. By using these, the structure of the ring of local invariants is determined, and complete sets of primary and secondary invariants are identified: there are 10 of the former and 15 of the latter.
1751-8113
10083-10108
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Welsh, T.A.
3f6176e0-a8b3-4df3-92a3-99d543576db1
Jarvis, P.D.
99bb8f36-d7dd-4a55-b7e9-99bf6b3428c2
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Welsh, T.A.
3f6176e0-a8b3-4df3-92a3-99d543576db1
Jarvis, P.D.
99bb8f36-d7dd-4a55-b7e9-99bf6b3428c2

King, R.C., Welsh, T.A. and Jarvis, P.D. (2007) The mixed two-qubit system and the structure of its ring of local invariants. Journal of Physics A: Mathematical and Theoretical, 40 (33), 10083-10108. (doi:10.1088/1751-8113/40/33/011).

Record type: Article

Abstract

The local invariants of a mixed two-qubit system are discussed. These invariants are polynomials in the elements of the corresponding density matrix. They are counted by means of group-theoretic branching rules which relate this problem to one arising in spin-isospin nuclear shell models. The corresponding Molien series and a refinement in the form of a 4-parameter generating function are determined. A graphical approach is then used to construct explicitly a fundamental set of 21 invariants. Relations between them are found in the form of syzygies. By using these, the structure of the ring of local invariants is determined, and complete sets of primary and secondary invariants are identified: there are 10 of the former and 15 of the latter.

Text
jpa2007_40_10083.pdf - Version of Record
Restricted to Repository staff only

More information

Published date: 1 August 2007

Identifiers

Local EPrints ID: 47927
URI: http://eprints.soton.ac.uk/id/eprint/47927
ISSN: 1751-8113
PURE UUID: 275b7023-2048-49df-8d7f-87803a049327

Catalogue record

Date deposited: 10 Aug 2007
Last modified: 08 Jan 2022 01:10

Export record

Altmetrics

Contributors

Author: R.C. King
Author: T.A. Welsh
Author: P.D. Jarvis

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×