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.
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).
GET FULL TEXT PDFREAD ON ARXIV VANITY
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
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 language | English |
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Number of pages | 42 |
Journal | Quantum |
Volume | 5 |
Issue number | 450 |
DOIs | |
Publication status | Published - 1 May 2021 |