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

Maciej Demianowicz
Phys. Rev. A 106, 012442 – Published 29 July 2022

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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  • Received 22 February 2022
  • Revised 11 May 2022
  • Accepted 10 June 2022

DOI:https://doi.org/10.1103/PhysRevA.106.012442

©2022 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Maciej Demianowicz*

  • Institute of Physics and Applied Computer Science, Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland

  • *maciej.demianowicz@pg.edu.pl

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Vol. 106, Iss. 1 — July 2022

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