A complete set of covariants of the four qubit system

Details A complete set of covariants of the four qubit system A complete set of covariants of the four qubit system

2003-04-03

arxiv.org/abs/quant-ph/0304026v3

Physics

Quantum Physics

14 pages, IOP macros; slightly expanded version

Scientific paper

10.1088/0305-4470/36/38/309

We obtain a complete and minimal set of 170 generators for the algebra of $SL(2,\C)^{\times 4}$-covariants of a binary quadrilinear form. Interpreted in terms of a four qubit system, this describes in particular the algebraic varieties formed by the orbits of local filtering operations in its projective Hilbert space. Also, this sheds some light on the local unitary invariants, and provides all the possible building blocks for the construction of entanglement measures for such a system.

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