k-stretchability of entanglement, and the duality of k-separability and k-producibility
The notions of $k$-separability and $k$-producibility are useful and expressive tools for the characterization of entanglement in multipartite quantum systems, when a more detailed analysis would be infeasible or simply needless. In this work we reveal a partial duality between them, which is valid...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2019-12-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2019-12-02-204/pdf/ |
| _version_ | 1818368931637755904 |
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| author | Szilárd Szalay |
| author_facet | Szilárd Szalay |
| author_sort | Szilárd Szalay |
| collection | DOAJ |
| description | The notions of $k$-separability and $k$-producibility are useful and expressive tools for the characterization of entanglement in multipartite quantum systems, when a more detailed analysis would be infeasible or simply needless. In this work we reveal a partial duality between them, which is valid also for their correlation counterparts. This duality can be seen from a much wider perspective, when we consider the entanglement and correlation properties which are invariant under the permutations of the subsystems. These properties are labeled by Young diagrams, which we endow with a refinement-like partial order, to build up their classification scheme. This general treatment reveals a new property, which we call $k$-stretchability, being sensitive in a balanced way to both the maximal size of correlated (or entangled) subsystems and the minimal number of subsystems uncorrelated with (or separable from) one another. |
| first_indexed | 2024-12-13T23:15:47Z |
| format | Article |
| id | doaj.art-5a9a58746a3a4affba8a26296c7942a9 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-13T23:15:47Z |
| publishDate | 2019-12-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-5a9a58746a3a4affba8a26296c7942a92022-12-21T23:27:56ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2019-12-01320410.22331/q-2019-12-02-20410.22331/q-2019-12-02-204k-stretchability of entanglement, and the duality of k-separability and k-producibilitySzilárd SzalayThe notions of $k$-separability and $k$-producibility are useful and expressive tools for the characterization of entanglement in multipartite quantum systems, when a more detailed analysis would be infeasible or simply needless. In this work we reveal a partial duality between them, which is valid also for their correlation counterparts. This duality can be seen from a much wider perspective, when we consider the entanglement and correlation properties which are invariant under the permutations of the subsystems. These properties are labeled by Young diagrams, which we endow with a refinement-like partial order, to build up their classification scheme. This general treatment reveals a new property, which we call $k$-stretchability, being sensitive in a balanced way to both the maximal size of correlated (or entangled) subsystems and the minimal number of subsystems uncorrelated with (or separable from) one another.https://quantum-journal.org/papers/q-2019-12-02-204/pdf/ |
| spellingShingle | Szilárd Szalay k-stretchability of entanglement, and the duality of k-separability and k-producibility Quantum |
| title | k-stretchability of entanglement, and the duality of k-separability and k-producibility |
| title_full | k-stretchability of entanglement, and the duality of k-separability and k-producibility |
| title_fullStr | k-stretchability of entanglement, and the duality of k-separability and k-producibility |
| title_full_unstemmed | k-stretchability of entanglement, and the duality of k-separability and k-producibility |
| title_short | k-stretchability of entanglement, and the duality of k-separability and k-producibility |
| title_sort | k stretchability of entanglement and the duality of k separability and k producibility |
| url | https://quantum-journal.org/papers/q-2019-12-02-204/pdf/ |
| work_keys_str_mv | AT szilardszalay kstretchabilityofentanglementandthedualityofkseparabilityandkproducibility |