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

5 Citations (Scopus)

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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