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


King, RC and Welsh, TA and Jarvis, PD, The mixed two-qubit system and the structure of its ring of local invariants, Journal of Physics A: Mathematical and Theoretical, 40, (33) pp. 10083-10108. ISSN 1751-8113 (2007) [Refereed Article]

DOI: doi:10.1088/1751-8113/40/33/011


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 four-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. © 2007 IOP Publishing Ltd.

Item Details

Item Type:Refereed Article
Research Division:Physical Sciences
Research Group:Other physical sciences
Research Field:Other physical sciences not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the physical sciences
UTAS Author:Jarvis, PD (Dr Peter Jarvis)
ID Code:46021
Year Published:2007
Web of Science® Times Cited:11
Deposited By:Physics
Deposited On:2007-08-01
Last Modified:2008-04-04

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