Quantum bidding in Bridge

Abstract: Quantum methods allow to reduce communication complexity of some computational tasks, with several separated partners, beyond classical constraints. Nevertheless, experimental demonstrations of this fact are thus far limited to some abstract problems, far away from real-life tasks. We show here, and demonstrate experimentally, that the power of reduction of communication complexity can be harnessed to gain advantage in famous, immensely popular, card game - Bridge. The essence of a winning strategy in Bridge is efficient communication between the partners. The rules of the game allow only specific form of communication, of a very low complexity (effectively one has a strong limitations on number of exchanged bits). Surprisingly, our quantum technique is not violating the existing rules of the game (as there is no increase in information flow). We show that our quantum Bridge auction corresponds to a biased nonlocal Clauser-Horne-Shimony-Holt (CHSH) game, which is equivalent to a $2\to 1$ quantum random access code. Thus our experiment is also a realization of such protocols. However, this correspondence is not full which enables the Bridge players to have efficient strategies regardless of the quality of their detectors.