Fully non-positive-partial-transpose genuinely entangled subspaces

Owidiusz Makuta, Błażej Kuzaka, and Remigiusz Augusiak

Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland

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Abstract

Genuinely entangled subspaces are a class of subspaces in the multipartite Hilbert spaces that are composed of only genuinely entangled states. They are thus an interesting object of study in the context of multipartite entanglement. Here we provide a construction of multipartite subspaces that are not only genuinely entangled but also fully non-positive-partial-transpose (NPT) in the sense that any mixed state supported on them has non-positive partial transpose across any bipartition. Our construction originates from the stabilizer formalism known for its use in quantum error correction. To this end, we first introduce a couple of criteria allowing to assess whether any state from a given non-trivial stabilizer subspace is genuinely multipartite entangled. We then use these criteria to construct genuinely entangled stabilizer subspaces for any number of parties and arbitrary local dimension and conjecture them to be of maximal dimension achievable within the stabilizer formalism. At the same time, we prove that every genuinely entangled subspace is fully NPT in the above sense, which implies a quite surprising fact that no genuinely entangled stabilizer subspace can support PPT entangled states.

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Cited by

[1] Fabian Bernards and Otfried Gühne, "Multiparticle singlet states cannot be maximally entangled for the bipartitions", Journal of Mathematical Physics 65 1, 012201 (2024).

[2] K. V. Antipin, "On generating r-uniform subspaces with the isometric mapping method", Modern Physics Letters A 39 02, 2350185 (2024).

[3] Maciej Demianowicz, "Universal construction of genuinely entangled subspaces of any size", Quantum 6, 854 (2022).

[4] K. V. Antipin, "On generating r-uniform subspaces with the isometric mapping method", arXiv:2301.03120, (2023).

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