License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.82
URN: urn:nbn:de:0030-drops-141514
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14151/
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Jee, Hyejung H. ; Sparaciari, Carlo ; Fawzi, Omar ; Berta, Mario

Quasi-Polynomial Time Algorithms for Free Quantum Games in Bounded Dimension

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LIPIcs-ICALP-2021-82.pdf (0.7 MB)


Abstract

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.

BibTeX - Entry

@InProceedings{jee_et_al:LIPIcs.ICALP.2021.82,
  author =	{Jee, Hyejung H. and Sparaciari, Carlo and Fawzi, Omar and Berta, Mario},
  title =	{{Quasi-Polynomial Time Algorithms for Free Quantum Games in Bounded Dimension}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{82:1--82:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14151},
  URN =		{urn:nbn:de:0030-drops-141514},
  doi =		{10.4230/LIPIcs.ICALP.2021.82},
  annote =	{Keywords: non-local game, semidefinite programming, quantum correlation, approximation algorithm, Lasserre hierarchy, de Finetti theorem}
}

Keywords: non-local game, semidefinite programming, quantum correlation, approximation algorithm, Lasserre hierarchy, de Finetti theorem
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021


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