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Communication Dans Un Congrès Année : 2021

Quasi-polynomial time algorithms for free quantum games in bounded dimension

Résumé

We give a converging semidefinite programming hierarchy of outer approximations for the set of quantum correlations of fixed dimension and derive analytical bounds on the convergence speed of the hierarchy. In particular, we give a semidefinite program of size $\exp(\mathcal{O}\big(T^{12}(\log^2(AT)+\log(Q)\log(AT))/\epsilon^2\big))$ to compute additive $\epsilon$-approximations on the values of two-player free games with $T\times T$-dimensional quantum assistance, where $A$ and $Q$ denote the numbers 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. We also derive an informationally complete measurement which minimises the loss in distinguishability relative to the quantum side information - which may be of independent interest.

Dates et versions

hal-03130069 , version 1 (03-02-2021)

Identifiants

Citer

Hyejung Jee, Carlo Sparaciari, Omar Fawzi, Mario Berta. Quasi-polynomial time algorithms for free quantum games in bounded dimension. 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021), Jul 2021, Glasgow, United Kingdom. ⟨10.4230/LIPIcs.ICALP.2021.82⟩. ⟨hal-03130069⟩
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