Distillation of entanglement by projection on permutationally invariant subspaces

Abstract

We consider distillation of entanglement from two qubit states which are mixtures of three mutually orthogonal states: two pure entangled states and one pure product state. 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. 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. to 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.

22 pages, comments welcome

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Cited by in corpus (3)

• Simplified formalism of the algebra of partially transposed permutation operators with applications
• Effect of weak measurement on entanglement distribution over noisy channels
• Explicit constructions of unitary transformations between equivalent irreducible representations