A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios
Correlations in Einstein-Podolsky-Rosen (EPR) scenarios, captured by $assemblages$ of unnormalised quantum states, have recently caught the attention of the community, both from a foundational and an information-theoretic perspective. The set of quantum-realisable assemblages, or abbreviated to quan...
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-01-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-01-14-1591/pdf/ |
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| author | Matty J. Hoban Tom Drescher Ana Belén Sainz |
| author_facet | Matty J. Hoban Tom Drescher Ana Belén Sainz |
| author_sort | Matty J. Hoban |
| collection | DOAJ |
| description | Correlations in Einstein-Podolsky-Rosen (EPR) scenarios, captured by $assemblages$ of unnormalised quantum states, have recently caught the attention of the community, both from a foundational and an information-theoretic perspective. The set of quantum-realisable assemblages, or abbreviated to quantum assemblages, are those that arise from multiple parties performing local measurements on a shared quantum system. In general, deciding whether or not a given assemblage is a quantum assemblage, i.e. membership of the set of quantum assemblages, is a hard problem, and not always solvable. In this paper we introduce a hierarchy of tests where each level either determines non-membership of the set of quantum assemblages or is inconclusive. The higher the level of the hierarchy the better one can determine non-membership, and this hierarchy converges to a particular set of assemblages. Furthermore, this set to which it converges contains the quantum assemblages. Each test in the hierarchy is formulated as a semidefinite program. This hierarchy allows one to upper bound the quantum violation of a steering inequality and the quantum advantage provided by quantum EPR assemblages in a communication or information-processing task. |
| format | Article |
| id | doaj-art-46f38f9a686a4e41b55f6c1f8b4deff8 |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-46f38f9a686a4e41b55f6c1f8b4deff82025-01-14T15:21:33ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-01-019159110.22331/q-2025-01-14-159110.22331/q-2025-01-14-1591A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenariosMatty J. HobanTom DrescherAna Belén SainzCorrelations in Einstein-Podolsky-Rosen (EPR) scenarios, captured by $assemblages$ of unnormalised quantum states, have recently caught the attention of the community, both from a foundational and an information-theoretic perspective. The set of quantum-realisable assemblages, or abbreviated to quantum assemblages, are those that arise from multiple parties performing local measurements on a shared quantum system. In general, deciding whether or not a given assemblage is a quantum assemblage, i.e. membership of the set of quantum assemblages, is a hard problem, and not always solvable. In this paper we introduce a hierarchy of tests where each level either determines non-membership of the set of quantum assemblages or is inconclusive. The higher the level of the hierarchy the better one can determine non-membership, and this hierarchy converges to a particular set of assemblages. Furthermore, this set to which it converges contains the quantum assemblages. Each test in the hierarchy is formulated as a semidefinite program. This hierarchy allows one to upper bound the quantum violation of a steering inequality and the quantum advantage provided by quantum EPR assemblages in a communication or information-processing task.https://quantum-journal.org/papers/q-2025-01-14-1591/pdf/ |
| spellingShingle | Matty J. Hoban Tom Drescher Ana Belén Sainz A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios Quantum |
| title | A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios |
| title_full | A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios |
| title_fullStr | A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios |
| title_full_unstemmed | A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios |
| title_short | A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios |
| title_sort | hierarchy of semidefinite programs for generalised einstein podolsky rosen scenarios |
| url | https://quantum-journal.org/papers/q-2025-01-14-1591/pdf/ |
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