Dear all,
all of next week we have two visitors who study entanglement with methods from representation theory. They will each give a talk, which I herewith announce.
Tuesday, 13th July, 11am, HIT K 51
Speaker: Graeme Mitchison
Title: The structure of local unitary invariants for qubit states.
Abstract: Local unitary invariants, i.e. real-valued functions of states that are invariant under local unitary action, can be regarded as entanglement measures. They have a rich structure, even for pure n-qubit states. I show that there is a fundamental family of invariants based on polynomials called cumulants. They have nice properties and account for about half of the total number for a complete set of invariants. They also have a hierarchical structure related to tracing out subsystems. I argue that this helps us understand the whole set of invariants and casts light on entanglement.
Wednesday, 14th July, 11am, HIT K 51
Speaker: Alonso Botero
Title: Weyl-Schur duality and asymptotic multipartite entanglement
Abstract: Through the so-called Weyl-Schur decomposition of n-fold tensor product Hilbert spaces, it is possible to connect various asymptotic rates of significance in Quantum Information Theory with the dimensions of certain "typical" invariant subspaces carrying irreducible representations of the permutation group. In this talk, I suggest a framework for the analysis of multipartite entanglement based on a similar application of the Weyl-Schur decomposition to the n-fold product of a multipartite state. Within this framework, it is possible to connect LU and SLOCC invariants to asymptotic rates and other quantities having a clear operational significance in terms of the resulting "typical" entanglement structures. These structures also suggest interesting connections between multipartite entanglement concentration, certain structures in algebraic combinatorics (Kronecker coefficients, Planar Transport problems, Association Schemes, etc.), and the theory of discrete orthogonal polynomials. I will try to give a brief overview of these connections and some partial results we have obtained in the three-qubit case.
Best wishes, Matthias.
Matthias Christandl
Institute for Theoretical Physics
ETH Zurich