A simplified formalism of the algebra of partially transposed permutation operators with applications

Marek Mozrzymas , Michał Studziński , Michał Horodecki

Abstract

Herein we continue the study of the representation theory of the algebra of permutation operators acting on the n-fold tensor product space, partially transposed on the last subsystem. 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 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. We also find relatively simple matrix representations for the generators of the underlying algebra. The obtained simplifications and developments are applied to derive the characteristics of a deterministic portbased teleportation scheme written purely in terms of irreducible representations of the studied 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. 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.
Author Marek Mozrzymas
Marek Mozrzymas,,
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, Michał Studziński
Michał Studziński,,
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, Michał Horodecki (FMPI / ITPA)
Michał Horodecki,,
- Institute of Theoretical Physics and Astrophysics
Journal seriesJournal of Physics A-Mathematical and Theoretical, ISSN 1751-8113, (A 25 pkt)
Issue year2018
Vol51
No12
Pages1-32
Publication size in sheets1.55
Keywords in Englishsymmetric group, irreducible representation, port-based teleportation
DOIDOI:10.1088/1751-8121/aaad15
URL https://doi.org/10.1088/1751-8121/aaad15
Languageen angielski
Score (nominal)30
ScoreMinisterial score = 25.0, 24-10-2018, ArticleFromJournal
Ministerial score (2013-2016) = 30.0, 24-10-2018, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 1.857 (2) - 2016=1.605 (5)
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