The Holographic Entropy Arrangement
Abstract
Here, we develop a convenient framework for characterizing multipartite entanglement in composite systems, based on relations between entropies of various subsystems. This continues the program initiated in [1], of using holography to effectively recast the geometric problem into an algebraic one. We prove that, for an arbitrary number of parties, our procedure identifies a finite set of entropic information quantities that we conveniently represent geometrically in the form of an arrangement of hyperplanes. This leads us to define the holographic entropy arrangement, whose algebraic and combinatorial aspects we explore in detail. Using the framework, we derive three new information quantities for four parties, as well as a new infinite family for any number of parties. A natural construct from the arrangement is the holographic entropy polyhedron which captures holographic entropy inequalities describing the physically allowed region of entropy space. We illustrate how to obtain the polyhedron by winnowing down the arrangement through a sieve to pick out candidate sign-definite information quantities. Comparing the polyhedron with the holographic entropy cone, we find perfect agreement for 4 parties and corroborating evidence for the conjectured 5-party entropy cone. Lastly, we work with explicit configurations in arbitrary (time-dependent) states leading to both simple derivationsmore »
- Authors:
-
- Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)
- Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)
- Univ. of California, Santa Barbara, CA (United States)
- Publication Date:
- Research Org.:
- Univ. of California, Davis, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF)
- OSTI Identifier:
- 1596290
- Alternate Identifier(s):
- OSTI ID: 1497238
- Grant/Contract Number:
- SC0009999; SC0019480; PHY17‐48958
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Fortschritte der Physik
- Additional Journal Information:
- Journal Volume: 67; Journal Issue: 4; Journal ID: ISSN 0015-8208
- Publisher:
- Wiley
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; holography; multipartite entanglement
Citation Formats
Hubeny, Veronika E., Rangamani, Mukund, and Rota, Massimiliano. The Holographic Entropy Arrangement. United States: N. p., 2019.
Web. doi:10.1002/prop.201900011.
Hubeny, Veronika E., Rangamani, Mukund, & Rota, Massimiliano. The Holographic Entropy Arrangement. United States. https://doi.org/10.1002/prop.201900011
Hubeny, Veronika E., Rangamani, Mukund, and Rota, Massimiliano. Wed .
"The Holographic Entropy Arrangement". United States. https://doi.org/10.1002/prop.201900011. https://www.osti.gov/servlets/purl/1596290.
@article{osti_1596290,
title = {The Holographic Entropy Arrangement},
author = {Hubeny, Veronika E. and Rangamani, Mukund and Rota, Massimiliano},
abstractNote = {Here, we develop a convenient framework for characterizing multipartite entanglement in composite systems, based on relations between entropies of various subsystems. This continues the program initiated in [1], of using holography to effectively recast the geometric problem into an algebraic one. We prove that, for an arbitrary number of parties, our procedure identifies a finite set of entropic information quantities that we conveniently represent geometrically in the form of an arrangement of hyperplanes. This leads us to define the holographic entropy arrangement, whose algebraic and combinatorial aspects we explore in detail. Using the framework, we derive three new information quantities for four parties, as well as a new infinite family for any number of parties. A natural construct from the arrangement is the holographic entropy polyhedron which captures holographic entropy inequalities describing the physically allowed region of entropy space. We illustrate how to obtain the polyhedron by winnowing down the arrangement through a sieve to pick out candidate sign-definite information quantities. Comparing the polyhedron with the holographic entropy cone, we find perfect agreement for 4 parties and corroborating evidence for the conjectured 5-party entropy cone. Lastly, we work with explicit configurations in arbitrary (time-dependent) states leading to both simple derivations and an intuitive picture of the entanglement pattern.},
doi = {10.1002/prop.201900011},
journal = {Fortschritte der Physik},
number = 4,
volume = 67,
place = {United States},
year = {Wed Feb 27 00:00:00 EST 2019},
month = {Wed Feb 27 00:00:00 EST 2019}
}
Web of Science
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