On the relation between the subadditivity cone and the quantum entropy cone
Abstract Given a multipartite quantum system, what are the possible ways to impose mutual independence among some subsystems, and the presence of correlations among others, such that there exists a quantum state which satisfies these demands? This question and the related notion of a pattern of marg...
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SpringerOpen
2023-08-01
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Series: | Journal of High Energy Physics |
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Online Access: | https://doi.org/10.1007/JHEP08(2023)018 |
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author | Temple He Veronika E. Hubeny Massimiliano Rota |
author_facet | Temple He Veronika E. Hubeny Massimiliano Rota |
author_sort | Temple He |
collection | DOAJ |
description | Abstract Given a multipartite quantum system, what are the possible ways to impose mutual independence among some subsystems, and the presence of correlations among others, such that there exists a quantum state which satisfies these demands? This question and the related notion of a pattern of marginal independence (PMI) were introduced in [1], and then argued in [2] to be central in the derivation of the holographic entropy cone. Here we continue the general information theoretic analysis of the PMIs allowed by strong subadditivity (SSA) initiated in [1]. We show how the computation of these PMIs simplifies when SSA is replaced by a weaker constraint, dubbed Klein’s condition (KC), which follows from the necessary condition for the saturation of subadditivity (SA). Formulating KC in the language of partially ordered sets, we show that the set of PMIs compatible with KC forms a lattice, and we investigate several of its structural properties. One of our main results is the identification of a specific lower dimensional face of the SA cone that contains on its boundary all the extreme rays (beyond Bell pairs) that can possibly be realized by quantum states. We verify that for four or more parties, KC is strictly weaker than SSA, but nonetheless the PMIs compatible with SSA can easily be derived from the KC-compatible ones. For the special case of 1-dimensional PMIs, we conjecture that KC and SSA are in fact equivalent. To make the presentation self-contained, we review the key ingredients from lattice theory as needed. |
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institution | Directory Open Access Journal |
issn | 1029-8479 |
language | English |
last_indexed | 2024-03-11T15:16:53Z |
publishDate | 2023-08-01 |
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series | Journal of High Energy Physics |
spelling | doaj.art-7edcf263d9f04793bd00ab9f32768f222023-10-29T12:10:31ZengSpringerOpenJournal of High Energy Physics1029-84792023-08-012023815610.1007/JHEP08(2023)018On the relation between the subadditivity cone and the quantum entropy coneTemple He0Veronika E. Hubeny1Massimiliano Rota2Walter Burke Institute for Theoretical Physics, California Institute of TechnologyCenter for Quantum Mathematics and Physics (QMAP), Department of Physics & Astronomy, University of CaliforniaInstitute for Theoretical Physics, University of AmsterdamAbstract Given a multipartite quantum system, what are the possible ways to impose mutual independence among some subsystems, and the presence of correlations among others, such that there exists a quantum state which satisfies these demands? This question and the related notion of a pattern of marginal independence (PMI) were introduced in [1], and then argued in [2] to be central in the derivation of the holographic entropy cone. Here we continue the general information theoretic analysis of the PMIs allowed by strong subadditivity (SSA) initiated in [1]. We show how the computation of these PMIs simplifies when SSA is replaced by a weaker constraint, dubbed Klein’s condition (KC), which follows from the necessary condition for the saturation of subadditivity (SA). Formulating KC in the language of partially ordered sets, we show that the set of PMIs compatible with KC forms a lattice, and we investigate several of its structural properties. One of our main results is the identification of a specific lower dimensional face of the SA cone that contains on its boundary all the extreme rays (beyond Bell pairs) that can possibly be realized by quantum states. We verify that for four or more parties, KC is strictly weaker than SSA, but nonetheless the PMIs compatible with SSA can easily be derived from the KC-compatible ones. For the special case of 1-dimensional PMIs, we conjecture that KC and SSA are in fact equivalent. To make the presentation self-contained, we review the key ingredients from lattice theory as needed.https://doi.org/10.1007/JHEP08(2023)018AdS-CFT CorrespondenceDuality in Gauge Field Theories |
spellingShingle | Temple He Veronika E. Hubeny Massimiliano Rota On the relation between the subadditivity cone and the quantum entropy cone Journal of High Energy Physics AdS-CFT Correspondence Duality in Gauge Field Theories |
title | On the relation between the subadditivity cone and the quantum entropy cone |
title_full | On the relation between the subadditivity cone and the quantum entropy cone |
title_fullStr | On the relation between the subadditivity cone and the quantum entropy cone |
title_full_unstemmed | On the relation between the subadditivity cone and the quantum entropy cone |
title_short | On the relation between the subadditivity cone and the quantum entropy cone |
title_sort | on the relation between the subadditivity cone and the quantum entropy cone |
topic | AdS-CFT Correspondence Duality in Gauge Field Theories |
url | https://doi.org/10.1007/JHEP08(2023)018 |
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