Michal Studzinski, Nicolaus Copernicus University
Abstract:
We consider distillation of entanglement from two qubit states which are mixtures of two pure entangled states and one pure product state, which is orthogonal to them. We distill entanglement from such states by projecting n copies of the state on permutationally invariant subspace and then applying one-way hashing protocol. We find analytical expressions for the rate of the protocol and show that for wide range of parameters the protocol achieves higher rates than the previous ones. We also generalize this method to higher dimensional systems. To get analytical expression for two qubit case, we faced a mathematical problem of diagonalizing a family of matrices enjoying some symmetries w.r.t. the symmetric group. We have solved this problem in two ways: (i) directly, by use of Schur-Weyl decomposition and Young symmetrizers (ii) showing that the problem is equivalent to a problem of diagonalizing adjacency matrices in a particular instance of a so called algebraic association scheme.