Multiplayer Quantum Games

Played with atoms and photons rather than dice and coins, quantum games are contests whose outcomes are governed by the unusual logic of the submicroscopic world. The basic token in a quantum game is a "qubit," a bit of data which is stored in an object such as an atomic nucleus. While a classical coin can only be heads (data value 0) or tails (data value 1), a qubit can effectively be both heads (0) and tails (1) at the same time, since the nucleus can be in a combination or superposition of spin-up (0) and spin-down (1). What's more, one can interlink or "entangle" qubits held by separate players so that manipulating one qubit strongly affects the others.

More than a diversion, playing quantum games can reveal new information-processing tasks (possibly even certain types of financial transactions) that quantum computers could perform more efficiently than classical computers. Towards these ends, theorists have been taking traditional games, adapting them for the quantum realm, and checking if new or better strategies emerge for winning.

While past quantum games have focused on two players (Update 411), Oxford researchers (Patrick Hayden, patrick.hayden@qubit.org) have now identified multiplayer games in which the player's optimal strategy differs from that of the classical version of the game. The researchers discovered unique strategies in a three-player quantum version of the Dilemma game, in which three partners engaged in a venture (such as getting the best seats at a concert) each decide whether or not to betray the others in efforts to maximize personal gain.

In the quantum version, the qubits are entangled, then each person uses his qubit to choose between the following strategies: try for good seat (0), settle for poor seat (1) or some superposition of the two. Entanglement actually destroys the incentive for a player to contradict and thereby betray his opponents and it removes the classical dilemma entirely. Although quantum games are mostly played on paper at this point, a Chinese group has just reported the experimental realization of a quantum Prisoner's Dilemma (Los Alamos preprint). (Benjamin and Hayden, Physical Review A, September 2001.)