Fully non-positive-partial-transpose genuinely entangled subspaces
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...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-02-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-02-09-915/pdf/ |
| _version_ | 1811168160816037888 |
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| author | Owidiusz Makuta Błażej Kuzaka Remigiusz Augusiak |
| author_facet | Owidiusz Makuta Błażej Kuzaka Remigiusz Augusiak |
| author_sort | Owidiusz Makuta |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T16:21:26Z |
| format | Article |
| id | doaj.art-885e1ab373e24f0f97bf1302af4147c0 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-10T16:21:26Z |
| publishDate | 2023-02-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-885e1ab373e24f0f97bf1302af4147c02023-02-09T13:31:48ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-02-01791510.22331/q-2023-02-09-91510.22331/q-2023-02-09-915Fully non-positive-partial-transpose genuinely entangled subspacesOwidiusz MakutaBłażej KuzakaRemigiusz AugusiakGenuinely 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.https://quantum-journal.org/papers/q-2023-02-09-915/pdf/ |
| spellingShingle | Owidiusz Makuta Błażej Kuzaka Remigiusz Augusiak Fully non-positive-partial-transpose genuinely entangled subspaces Quantum |
| title | Fully non-positive-partial-transpose genuinely entangled subspaces |
| title_full | Fully non-positive-partial-transpose genuinely entangled subspaces |
| title_fullStr | Fully non-positive-partial-transpose genuinely entangled subspaces |
| title_full_unstemmed | Fully non-positive-partial-transpose genuinely entangled subspaces |
| title_short | Fully non-positive-partial-transpose genuinely entangled subspaces |
| title_sort | fully non positive partial transpose genuinely entangled subspaces |
| url | https://quantum-journal.org/papers/q-2023-02-09-915/pdf/ |
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