R C King et al 2007 J. Phys. A: Math. Theor. 40 10083 doi:10.1088/1751-8113/40/33/011
R C King1, T A Welsh1,3 and P D Jarvis2
Show affiliationsThe 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.
03.67.Lx Quantum computation architectures and implementations
81Rxx Groups and algebras in quantum theory
12D05 Polynomials: factorization
81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
Issue 33 (17 August 2007)
Received 7 May 2007, in final form 15 June 2007
Published 1 August 2007
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