Fair Game of Quantum Penny Flip

Abstract

The Quantum Penny Flip is a classic thought experiment in quantum mechanics that demonstrates the weird and counterintuitive nature of the quantum world. To solve the “PQ” problem, we proposed a quantum strategy selection and optimization algorithm, and designed a quantum algorithm for this problem. In terms of practical applications and Case study, this paper reviews the classic two player game – “PQ coin flipping” problem, and shows that when one of the participants adopts quantum strategies, he can defeat his classic opponent and obtain higher returns. By using quantitative methods, the entire “PQ” problem is placed under a more general and fair condition, and it is promoted and studied again from multiple aspects and perspectives. At the same time, this article provides the definitions of “incomplete fair game” and “complete fair game”, modifies the quantum coin flipping game [Meyer, Phys. Rev. lett. 82 (1999) 1052] to make the game fair, and studies the multi round versions of quantum coin flipping. We have drawn some basic conclusions about fair quantum games and explained the meaning of completely fair games in practice. We discussed the limitations and scalability of the “PQ” problem and looked forward to the future development direction of quantum game research.