Designing Quantum Game Strategies from Quantum Communication Protocols

摘要

In their recent paper, Cleve , Slofstra, Unger and Upadhyay showed that the CHSH~(⊕n), a natural extension of the CHSH game to the one with a scalable input, has an optimal worst-case winning probability of 1/2 + 0.5(1/(2~n)~(1/2)). Their game strategy is a simple parallelization of the original CHSH and needs n pairs of qubits for shared entanglement. In this paper, we present a new strategy whose worst-case winning probability is 1/2 + 0.46(1/(2~n)~(1/2)), a bit worse than theirs, but it needs only a single pair of qubits for shared entanglement. This is done by a nontrivial application of another recent result by Ambainis, Leung, Mancinska and Ozols about the (n, 1) quantum random access coding. We generalize this approach, namely we give a general conversion rule from a two-party quantum communication protocol with communication complexity one into a strategy for an XOR game with a single pair of entangled qubits. This enables us to design two more new strategies that also need minimum entanglement for CHSH~(⊕n).