Complexity Limitations on One-turn Quantum Refereed Games

This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send states to a referee, who performs an efficiently implementable joint measurement on the determine player wins. The class QRG(1) contains those decision problems for one can always win with high probability yes-instances and other no-instances, regardless opposing player’s strategy. trivially QMA ∪co-QMA is known be contained in PSPACE. We prove stronger containments restricted variants this class. Specifically, if limited sending classical (probabilistic) state rather than state, resulting CQRG(1) ∃⋅PP (the nondeterministic polynomial-time operator applied PP); while both but referee forced measure first, incorporates outcome into second MQRG(1) P ⋅PP unbounded-error probabilistic PP).