Negative result about the construction of genuinely entangled subspaces from unextendible product bases

Maciej Demianowicz

doi:10.1103/physreva.106.012442

Negative result about the construction of genuinely entangled subspaces from unextendible product bases

Abstract

Unextendible product bases (UPBs) provide a versatile tool with various applications across different areas of quantum information theory. Their comprehensive characterization is thus of great importance and has been a subject of vital interest for over two decades now. An open question asks about the existence of UPBs, which are genuinely unextendible, i.e., they are not extendible even with biproduct vectors. In other words, the problem is to verify whether there exist genuinely entangled subspaces (GESs), subspaces composed solely of genuinely multiparty entangled states, complementary to UPBs. We solve this problem in the negative for many sizes of UPBs in different multipartite scenarios. In particular, in the all-important case of equal local dimensions, we show that there are always forbidden cardinalities for such UPBs, including the minimal ones corresponding to GESs of the maximal dimensions.

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Maciej Demianowicz dr hab. inż.

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DOI:: Digital Object Identifier (open in new tab) 10.1103/physreva.106.012442
License: Copyright (2022 American Physical Society)

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Articles

Type:

artykuły w czasopismach

Published in:

PHYSICAL REVIEW A no. 106,
ISSN: 2469-9926

Language:

English

Publication year:

2022

Bibliographic description:

Demianowicz M.: Negative result about the construction of genuinely entangled subspaces from unextendible product bases// PHYSICAL REVIEW A -Vol. 106, (2022), s.012442-

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