![]() ![]() We also show a connection between the density operator characterising port-based teleportation and a particular matrix composed of an irreducible representation of the symmetric group, which encodes properties of the investigated algebra. We solve an eigenproblem for the generators of the algebra, which is the first step towards a hybrid port-based teleportation scheme and gives us new proofs of the asymptotic behaviour of teleportation fidelity. The obtained simplifications and developments are applied to derive the characteristics of a deterministic port-based teleportation scheme written purely in terms of irreducible representations of the studied algebra. We also find relatively simple matrix representations for the generators of the underlying algebra. Kitaev, Quantum computations: algorithms and error correction, Uspehi Mat. In our analysis we are able to reduce the complexity of the central expressions by getting rid of sums over all permutations from the symmetric group, obtaining equations which are much more handy in practical applications. Specifically: Definition 1 Let Hn be a 2n -dimensional Hilbert space (n qubits), and let C be a K-dimensional subspace of Hn. We develop the concept of partially reduced irreducible representations, which allows us to significantly simplify previously proved theorems and, most importantly, derive new results for irreducible representations of the mentioned algebra. In general, a quantum error-correcting code is a subspace of a Hilbert space designed so that any of a set of possible errors can be corrected by an appropriate quantum operation. ![]() Herein we continue the study of the representation theory of the algebra of permutation operators acting on the -fold tensor product space, partially transposed on the last subsystem. ![]()
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