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.
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
1 August 2007
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), .
(doi:10.1088/1751-8113/40/33/011).
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.
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Published date: 1 August 2007
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Local EPrints ID: 47927
URI: http://eprints.soton.ac.uk/id/eprint/47927
ISSN: 1751-8113
PURE UUID: 275b7023-2048-49df-8d7f-87803a049327
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Date deposited: 10 Aug 2007
Last modified: 15 Mar 2024 09:40
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Author:
R.C. King
Author:
T.A. Welsh
Author:
P.D. Jarvis
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