Designing Quantum Game Strategies from Quantum Communication Protocols

概要

論文の詳細を見る
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>). 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>), 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>.
2009-05-19