eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-07-02
82:1
82:20
10.4230/LIPIcs.ICALP.2021.82
article
Quasi-Polynomial Time Algorithms for Free Quantum Games in Bounded Dimension
Jee, Hyejung H.
1
Sparaciari, Carlo
1
2
Fawzi, Omar
3
Berta, Mario
1
4
5
Department of Computing, Imperial College London, UK
Department of Physics and Astronomy, University College London, UK
Univ Lyon, ENS Lyon, UCBL, CNRS, Inria, LIP, F-69342, Lyon Cedex 07, France
IQIM, California Institute of Technology, Pasadena, CA, USA
AWS Center for Quantum Computing, Pasadena, CA, USA
In a recent landmark result [Ji et al., arXiv:2001.04383 (2020)], it was shown that approximating the value of a two-player game is undecidable when the players are allowed to share quantum states of unbounded dimension. In this paper, we study the computational complexity of two-player games when the dimension of the quantum systems is bounded by T. More specifically, we give a semidefinite program of size exp(𝒪(T^{12}(log²(AT)+log(Q)log(AT))/ε²)) to compute additive ε-approximations on the value of two-player free games with T× T-dimensional quantum entanglement, where A and Q denote the number of answers and questions of the game, respectively. For fixed dimension T, this scales polynomially in Q and quasi-polynomially in A, thereby improving on previously known approximation algorithms for which worst-case run-time guarantees are at best exponential in Q and A. For the proof, we make a connection to the quantum separability problem and employ improved multipartite quantum de Finetti theorems with linear constraints that we derive via quantum entropy inequalities.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol198-icalp2021/LIPIcs.ICALP.2021.82/LIPIcs.ICALP.2021.82.pdf
non-local game
semidefinite programming
quantum correlation
approximation algorithm
Lasserre hierarchy
de Finetti theorem