Binding complexity and multiparty entanglement
Abstract
We introduce “binding complexity”, a new notion of circuit complexity which quantifies the difficulty of distributing entanglement among multiple parties, each consisting of many local degrees of freedom. We define binding complexity of a given state as the minimal number of quantum gates that must act between parties to prepare it. To illustrate the new notion we compute it in a toy model for a scalar field theory, using certain multiparty entangled states which are analogous to configurations that are known in AdS/CFT to correspond to multiboundary wormholes. Pursuing this analogy, we show that our states can be prepared by the Euclidean path integral in (0 + 1)-dimensional quantum mechanics on graphs with wormhole-like structure. We compute the binding complexity of our states by adapting the Euler-Arnold approach to Nielsen’s geometrization of gate counting, and find a scaling with entropy that resembles a result for the interior volume of holographic multiboundary wormholes. We also compute the binding complexity of general coherent states in perturbation theory, and show that for “double-trace deformations” of the Hamiltonian the effects resemble expansion of a wormhole interior in holographic theories.
- Authors:
-
[2];
- Univ. of Pennsylvania, Philadelphia, PA (United States); Vrije Univ. Brussel (VUB), and International Solvay Inst. (Belgium). Theoretische Natuurkunde
- Univ. of Pennsylvania, Philadelphia, PA (United States)
- Publication Date:
- Research Org.:
- Duke Univ., Durham, NC (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF); Simons Foundation; It From Qubit Simons Collaboration
- OSTI Identifier:
- 1609628
- Grant/Contract Number:
- FG02-05ER41367; DGE-1845298; PHY-1607611
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 2; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; AdS-CFT Correspondence; Black Holes
Citation Formats
Balasubramanian, Vijay, DeCross, Matthew, Kar, Arjun, and Parrikar, Onkar. Binding complexity and multiparty entanglement. United States: N. p., 2019.
Web. doi:10.1007/jhep02(2019)069.
Balasubramanian, Vijay, DeCross, Matthew, Kar, Arjun, & Parrikar, Onkar. Binding complexity and multiparty entanglement. United States. https://doi.org/10.1007/jhep02(2019)069
Balasubramanian, Vijay, DeCross, Matthew, Kar, Arjun, and Parrikar, Onkar. Tue .
"Binding complexity and multiparty entanglement". United States. https://doi.org/10.1007/jhep02(2019)069. https://www.osti.gov/servlets/purl/1609628.
@article{osti_1609628,
title = {Binding complexity and multiparty entanglement},
author = {Balasubramanian, Vijay and DeCross, Matthew and Kar, Arjun and Parrikar, Onkar},
abstractNote = {We introduce “binding complexity”, a new notion of circuit complexity which quantifies the difficulty of distributing entanglement among multiple parties, each consisting of many local degrees of freedom. We define binding complexity of a given state as the minimal number of quantum gates that must act between parties to prepare it. To illustrate the new notion we compute it in a toy model for a scalar field theory, using certain multiparty entangled states which are analogous to configurations that are known in AdS/CFT to correspond to multiboundary wormholes. Pursuing this analogy, we show that our states can be prepared by the Euclidean path integral in (0 + 1)-dimensional quantum mechanics on graphs with wormhole-like structure. We compute the binding complexity of our states by adapting the Euler-Arnold approach to Nielsen’s geometrization of gate counting, and find a scaling with entropy that resembles a result for the interior volume of holographic multiboundary wormholes. We also compute the binding complexity of general coherent states in perturbation theory, and show that for “double-trace deformations” of the Hamiltonian the effects resemble expansion of a wormhole interior in holographic theories.},
doi = {10.1007/jhep02(2019)069},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2019,
place = {United States},
year = {Tue Feb 12 00:00:00 EST 2019},
month = {Tue Feb 12 00:00:00 EST 2019}
}
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