An algebraically independent generating set of the algebra of local unitary invariants

Details An algebraically independent generating set of the algebra of local unitary invariants An algebraically independent generating set of the algebra of local unitary invariants

2011-02-14

arxiv.org/abs/1102.2861v1

Physics

Quantum Physics

6 pages

Scientific paper

We show that the inverse limit of the graded algebras of local unitary
invariant polynomials of finite dimensional k-partite quantum systems is free,
and give an algebraically independent generating set. The number of degree 2d
invariants in the generating set is equal to the number of conjugacy classes of
index d subgroups of a free group on k-1 generators.

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