Entanglement in Non-local Games and the Hyperlinear Profile of Groups

William Slofstra; Thomas Vidick

doi:10.1007/s00023-018-0718-y

Entanglement in Non-local Games and the Hyperlinear Profile of Groups

William Slofstra
, Thomas Vidick

Research output: Contribution to journal › Article › peer-review

Abstract

We relate the amount of entanglement required to play linear system non-local games near-optimally to the hyperlinear profile of finitely presented groups. By calculating the hyperlinear profile of a certain group, we give an example of a finite non-local game for which the amount of entanglement required to play -optimally is at least O(1/ k), for some k > 0. Since this function approaches infinity as approaches zero, this provides a quantitative version of a theorem of the first author.

Original language	English
Pages (from-to)	2979-3005
Number of pages	27
Journal	Annales Henri Poincare
Volume	19
Issue number	10
DOIs	https://doi.org/10.1007/s00023-018-0718-y
State	Published - 1 Oct 2018
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Nuclear and High Energy Physics
Mathematical Physics

Access to Document

10.1007/s00023-018-0718-y

http://arxiv.org/abs/1711.10676License: Other

Cite this

@article{171ac50f45eb491da4d39d9d0ddbbbec,

title = "Entanglement in Non-local Games and the Hyperlinear Profile of Groups",

abstract = "We relate the amount of entanglement required to play linear system non-local games near-optimally to the hyperlinear profile of finitely presented groups. By calculating the hyperlinear profile of a certain group, we give an example of a finite non-local game for which the amount of entanglement required to play -optimally is at least O(1/ k), for some k > 0. Since this function approaches infinity as approaches zero, this provides a quantitative version of a theorem of the first author. ",

author = "William Slofstra and Thomas Vidick",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Nature Switzerland AG.",

year = "2018",

month = oct,

day = "1",

doi = "10.1007/s00023-018-0718-y",

language = "الإنجليزيّة",

volume = "19",

pages = "2979--3005",

journal = "Annales Henri Poincare",

issn = "1424-0637",

publisher = "Birkhauser",

number = "10",

}

TY - JOUR

T1 - Entanglement in Non-local Games and the Hyperlinear Profile of Groups

AU - Slofstra, William

AU - Vidick, Thomas

PY - 2018/10/1

Y1 - 2018/10/1

N2 - We relate the amount of entanglement required to play linear system non-local games near-optimally to the hyperlinear profile of finitely presented groups. By calculating the hyperlinear profile of a certain group, we give an example of a finite non-local game for which the amount of entanglement required to play -optimally is at least O(1/ k), for some k > 0. Since this function approaches infinity as approaches zero, this provides a quantitative version of a theorem of the first author.

AB - We relate the amount of entanglement required to play linear system non-local games near-optimally to the hyperlinear profile of finitely presented groups. By calculating the hyperlinear profile of a certain group, we give an example of a finite non-local game for which the amount of entanglement required to play -optimally is at least O(1/ k), for some k > 0. Since this function approaches infinity as approaches zero, this provides a quantitative version of a theorem of the first author.

UR - https://www.scopus.com/pages/publications/85051650468

U2 - 10.1007/s00023-018-0718-y

DO - 10.1007/s00023-018-0718-y

M3 - مقالة

SN - 1424-0637

VL - 19

SP - 2979

EP - 3005

JO - Annales Henri Poincare

JF - Annales Henri Poincare

IS - 10

ER -

Entanglement in Non-local Games and the Hyperlinear Profile of Groups

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this