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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Main Authors: Temple He, Veronika E. Hubeny, Massimiliano Rota
Format: Article
Language:English
Published: SpringerOpen 2023-08-01
Series:Journal of High Energy Physics
Subjects:
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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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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