3 research outputs found
Unitary invariants of qubit systems
We give an algorithm allowing to construct bases of local unitary invariants
of pure k-qubit states from the knowledge of polynomial covariants of the group
of invertible local filtering operations. The simplest invariants obtained in
this way are explicited and compared to various known entanglement measures.
Complete sets of generators are obtained for up to four qubits, and the
structure of the invariant algebras is discussed in detail.Comment: 19 pages, 1 figur
Hopf algebras of diagrams
23 pages, LaTEXInternational audienceWe investigate several Hopf algebras of diagrams related to Quantum Field Theory of Partitions and whose product comes from the Hopf algebras WSym or WQSym respectively built on integer set partitions and set compositions. Bases of these algebras are indexed either by bipartite graphs (labelled or unlabbeled) or by packed matrices (with integer or set coefficients). Realizations on biword are exhibited, and it is shown how these algebras fit into a commutative diagram. Hopf deformations and dendriform structures are also considered for some algebras in the picture