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Irreducible representations of partially transposed permutation operators with applications to quantum information problems

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In this talk we show how to construct irreducible representations (irreps) of partially transposed permutation operators over last subsystem. We give direct method of irreps construction for an arbitrary number of subsystems n and local Hilbert space dimension d. Our method is inspired by representation theory of symmetric group, especially so called Schur-Weyl duality and Walled Brauer Algebras. At the end of the talk we consider one possible application of our tool to the problem of universal quantum cloning machines. Using group- theory formalism, we show that the allowed region for fidelities (describes quality of the clones) can be expressed in terms of overlaps of pure states with irreducible representations of the partially transposed permutation operators.

This talk is part of the CQIF Seminar series.

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