Brylinski, Jean-Luc; Brylinski, Ranee Invariant polynomial functions on \(k\) qubits. (English) Zbl 1075.81506 Chen, Goong (ed.) et al., Mathematics of quantum computation. Boca Raton, FL: Chapman & Hall/ CRC (ISBN 1-58488-282-4). Computational Mathematics Series, 277-286 (2002). The paper deals with polynomial functions on states in the tensor product of order \(k\) of \((\mathbb{C}^{n})\) which are invariant under the product \(G\) of special groups of local symmetries. One establishes conditions under which the subspace of \(G\)-invariants in the space of homogeneous degree \(d\) polynomial functions on tensor states is different from zero. Relation with generalized determinant function is put in evidence. Then one analyzes the limit as \(k\) increases, and one considers the special case when \(n=2\).For the entire collection see [Zbl 1077.81018]. Reviewer: Guy Jumarie (Montréal) Cited in 1 Document MSC: 81P68 Quantum computation PDFBibTeX XMLCite \textit{J.-L. Brylinski} and \textit{R. Brylinski}, in: Mathematics of quantum computation. Boca Raton, FL: Chapman \& Hall/ CRC. 277--286 (2002; Zbl 1075.81506) Full Text: arXiv Online Encyclopedia of Integer Sequences: Nonzero Hilbert function values for the invariant ring of 3 X 3 X 3 X 3 tensors.