Binding complexity and multiparty entanglement

Balasubramanian, Vijay; DeCross, Matthew; Kar, Arjun; Parrikar, Onkar

doi:10.1007/jhep02(2019)069

Binding complexity and multiparty entanglement

Journal Article · Tue Feb 12 00:00:00 EST 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep02(2019)069· OSTI ID:1609628

Balasubramanian, Vijay ^[1]; DeCross, Matthew ^[2]; ^[2]; Parrikar, Onkar ^[2]

Univ. of Pennsylvania, Philadelphia, PA (United States); Vrije Univ. Brussel (VUB), and International Solvay Inst. (Belgium). Theoretische Natuurkunde; DOE/OSTI
Univ. of Pennsylvania, Philadelphia, PA (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Duke Univ., Durham, NC (United States)

Sponsoring Organization:: It From Qubit Simons Collaboration; National Science Foundation (NSF); Simons Foundation; USDOE Office of Science (SC)

Grant/Contract Number:: FG02-05ER41367

OSTI ID:: 1609628

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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