Invariant Polynomial Functions on k qudits
نویسندگان
چکیده
We study the polynomial functions on tensor states in (Cn)⊗k which are invariant under SU(n). We describe the space of invariant polynomials in terms of symmetric group representations. For k even, the smallest degree for invariant polynomials is n and in degree n we find a natural generalization of the determinant. For n, d fixed, we describe the asymptotic behavior of the dimension of the space of invariants as k → ∞. We study in detail the space of homogeneous degree 4 invariant polynomial functions on (C2)⊗k.
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تاریخ انتشار 2000