Universal construction of genuinely entangled subspaces of any size

Maciej Demianowicz

doi:10.22331/q-2022-11-10-854

Universal construction of genuinely entangled subspaces of any size

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

Published:	2022-11-10, volume 6, page 854
Eprint:	arXiv:2111.10193v4
Doi:	https://doi.org/10.22331/q-2022-11-10-854
Citation:	Quantum 6, 854 (2022).

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Abstract

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.

► BibTeX data

@article{Demianowicz2022universal,
  doi = {10.22331/q-2022-11-10-854},
  url = {https://doi.org/10.22331/q-2022-11-10-854},
  title = {Universal construction of genuinely entangled subspaces of any size},
  author = {Demianowicz, Maciej},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {854},
  month = nov,
  year = {2022}
}

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

[4] Masoud Gharahi and Stefano Mancini, "Entangled Subspaces through Algebraic Geometry", Quantum 9, 1947 (2025).

[5] 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).

[6] Zong-Xing Xiong, Mao-Sheng Li, Bing Yu, Zhu-Jun Zheng, and Lvzhou Li, "Genuinely nonlocal sets with smallest cardinality", Physical Review A 114 1, 012410 (2026).

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

[8] Maciej Demianowicz, "Progress in the study of the (non)existence of genuinely unextendible product bases", Quantum Information Processing 25 2, 67 (2026).

[9] 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).

[10] Owidiusz Makuta and Remigiusz Augusiak, "All genuinely entangled stabilizer subspaces are multipartite fully nonlocal", npj Quantum Information 11 1, 144 (2025).

[11] Diego Forlivesi, Lorenzo Valentini, and Marco Chiani, "Performance Analysis of Quantum CSS Error-Correcting Codes via MacWilliams Identities", Quantum 9, 1950 (2025).

[12] Maciej Demianowicz, Kajetan Vogtt, and Remigiusz Augusiak, "Completely entangled subspaces of entanglement depth k", Physical Review A 110 1, 012403 (2024).

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[15] 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).

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

[17] Congcong Zheng, Ping Xu, Kun Wang, and Zaichen Zhang, "GHZ-W Genuinely Entangled Subspace Verification with Adaptive Local Measurements", arXiv:2412.19540, (2024).

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