Designing locally maximally entangled quantum states with arbitrary local symmetries

Oskar Slowik*, Adam Sawicki, Tomasz Maciazek

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

Designing locally maximally entangled quantum states with arbitrary local symmetries
Oskar Słowik1, Adam Sawicki1, and Tomasz Maciążek2

1Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
2School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG, UK

Published: 2021-05-01, volume 5, page 450
Eprint: arXiv:2011.04078v5
Doi: https://doi.org/10.22331/q-2021-05-01-450
Citation: Quantum 5, 450 (2021).
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Abstract

One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local symmetries. We show how to design critical states with arbitrarily large local unitary symmetry. We explain that such states can be realised in a quantum system of distinguishable traps with bosons or fermions occupying a finite number of modes. Then, local symmetries of the designed quantum state are equal to the unitary group of local mode operations acting diagonally on all traps. Therefore, such a group of symmetries is naturally protected against errors that occur in a physical realisation of mode operators. We also link our results with the existence of so-called strictly semistable states with particular asymptotic diagonal symmetries. Our main technical result states that the Nth tensor power of any irreducible representation of SU(N) contains a copy of the trivial representation. This is established via a direct combinatorial analysis of Littlewood-Richardson rules utilising certain combinatorial objects which we call telescopes.
Original languageEnglish
Number of pages42
JournalQuantum
Volume5
Issue number450
DOIs
Publication statusPublished - 1 May 2021

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