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

被引：9
|
作者：
Slofstra, William [1 ]
Vidick, Thomas [2 ]
机构：
[1] Univ Waterloo, Dept Pure Math, Inst Quantum Comp, Waterloo, ON, Canada
[2] CALTECH, Dept Comp & Math Sci, Pasadena, CA 91125 USA
来源：
ANNALES HENRI POINCARE | 2018年 / 19卷 / 10期
关键词：
BELL INEQUALITIES;
D O I：
10.1007/s00023-018-0718-y
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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.
引用
收藏
页码：2979 / 3005
页数：27
相关论文
共 50 条
  • [1] Entanglement in Non-local Games and the Hyperlinear Profile of Groups
    William Slofstra
    Thomas Vidick
    [J]. Annales Henri Poincaré, 2018, 19 : 2979 - 3005
  • [2] Extended non-local games and monogamy-of-entanglement games
    Johnston, Nathaniel
    Mittal, Rajat
    Russo, Vincent
    Watrous, John
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2016, 472 (2189):
  • [3] Lower bounds on the entanglement needed to play XOR non-local games
    Slofstra, William
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2011, 52 (10)
  • [4] Perfect Strategies for Non-Local Games
    Lupini, M.
    Mancinska, L.
    Paulsen, V. I.
    Roberson, D. E.
    Scarpa, G.
    Severini, S.
    Todorov, I. G.
    Winter, A.
    [J]. MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2020, 23 (01)
  • [5] Perfect Strategies for Non-Local Games
    M. Lupini
    L. Mančinska
    V. I. Paulsen
    D. E. Roberson
    G. Scarpa
    S. Severini
    I. G. Todorov
    A. Winter
    [J]. Mathematical Physics, Analysis and Geometry, 2020, 23
  • [6] Two Party Non-Local Games
    Chakrabarty, I.
    Choudhury, B. S.
    [J]. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2008, 47 (12) : 3144 - 3149
  • [7] Two Party Non-Local Games
    I. Chakrabarty
    B. S. Choudhury
    [J]. International Journal of Theoretical Physics, 2008, 47 : 3144 - 3149
  • [8] Synchronicity for quantum non-local games
    Brannan, Michael
    Harris, Samuel J.
    Todorov, Ivan G.
    Turowska, Lyudmila
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2023, 284 (02)
  • [9] Complexity and entanglement in non-local computation and holography
    May, Alex
    [J]. QUANTUM, 2022, 6
  • [10] Non-local spin entanglement in a fermionic chain
    Jana, Sayan
    Varma, Anant V.
    Saha, Arijit
    Das, Sourin
    [J]. QUANTUM INFORMATION PROCESSING, 2022, 21 (11)
12345