Universal construction of genuinely entangled subspaces of any size

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

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We put forward a simple construction of genuinely entangled subspaces – subspaces supporting only genuinely multipartite entangled states – of any permissible dimensionality for any number of parties and local dimensions. The method uses nonorthogonal product bases, which are built from totally nonsingular matrices with a certain structure. We give an explicit basis for the constructed subspaces. An immediate consequence of our result is the possibility of constructing in the general multiparty scenario genuinely multiparty entangled mixed states with ranks up to the maximal dimension of a genuinely entangled subspace.

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Cited by

[1] Owidiusz Makuta, Błażej Kuzaka, and Remigiusz Augusiak, "Fully non-positive-partial-transpose genuinely entangled subspaces", Quantum 7, 915 (2023).

[2] Fei Shi, Ge Bai, Xiande Zhang, Qi Zhao, and Giulio Chiribella, "Graph-theoretic characterization of unextendible product bases", Physical Review Research 5 3, 033144 (2023).

[3] Mohamed Nawareg, "Completely entangled subspaces from Moore-like matrices", Physica Scripta 98 9, 095111 (2023).

[4] Sumit Nandi, Debashis Saha, Dipankar Home, and A. S. Majumdar, "Wigner-approach-enabled detection of multipartite nonlocality using all different bipartitions", Physical Review A 106 6, 062203 (2022).

[5] Maciej Demianowicz, "Negative result about the construction of genuinely entangled subspaces from unextendible product bases", Physical Review A 106 1, 012442 (2022).

[6] K. V. Antipin, "Construction of genuinely entangled multipartite subspaces from bipartite ones by reducing the total number of separated parties", Physics Letters A 445, 128248 (2022).

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