Quantum free games
Anand Natarajan, Tina Zhang

TL;DR
This paper advances the understanding of quantum free games by establishing new protocols and complexity class characterizations, including tight bounds for entangled and unentangled quantum proof systems, with implications for computational complexity.
Contribution
It provides new protocols and complexity class characterizations for quantum free games, including tight bounds and optimality results for entangled and unentangled quantum proof systems.
Findings
A BellQMA(2) protocol for 3SAT with $ ilde{O}(\sqrt{n})$ communication.
AM* with 2 provers and constant questions equals RE, as powerful as general entangled games.
Zero-gap AM* protocol for a $\Pi_2$ complete language with constant questions and logarithmic answers.
Abstract
The complexity of free games with two or more classical players was essentially settled by Aaronson, Impagliazzo, and Moshkovitz (CCC'14). There are two complexity classes that can be considered quantum analogues of classical free games: (1) AM*, the multiprover interactive proof class corresponding to free games with entangled players, and, somewhat less obviously, (2) BellQMA(2), the class of quantum Merlin-Arthur proof systems with two unentangled Merlins, whose proof states are separately measured by Arthur. In this work, we make significant progress towards a tight characterization of both of these classes. 1. We show a BellQMA(2) protocol for 3SAT on variables, where the total amount of communication is . This answers an open question of Chen and Drucker (2010) and also shows, conditional on ETH, that the algorithm of Brand\~{a}o, Christandl and Yard…
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Logic, programming, and type systems · Quantum Computing Algorithms and Architecture
