Quantum board games

Biao Wu, Hanbo Chen, Zhikang Luo

Maor Ganz, Or Sattath

A quantum board game is a multi-round protocol between a single quantum player against the quantum board. Molina and Watrous discovered quantum hedging. They gave an example for perfect quantum hedging: a board game with winning probability < 1, such that the player can win with certainty at least 1-out-of-2 quantum board games played in parallel. Here we show that perfect quantum hedging occurs in a cryptographic protocol – quantum coin flipping. For this reason, when cryptographic protocols are composed in parallel, hedging may introduce serious challenges into their analysis. We also show that hedging cannot occur when playing two-outcome board games in sequence. This is done by showing a formula for the value of sequential two-outcome board games, which depends only on the optimal value of a single board game; this formula applies in a more general setting of possible target functions, in which hedging is only a special case.

Παναγιώτης Αποστολίδης, Εύαγγελος Κ. Κοντονικολάου

André Ranchin

We introduce a new board game based on the ancient Chinese game of Go (Weiqi, Igo, Baduk). The key difference from the original game is that players no longer alternatively play single stones on the board but instead they take turns placing pairs of entangled go stones. A phenomenon of quantum-like collapse occurs when one of the stones in an entangled pair is directly in contact with at least one other stone. The player to whom the entangled pair belongs must then remove one of the stones in the pair from the board. The aim of the game is still to surround more territory than the opponent and as the number of stones increases, all the entangled pairs of stones eventually reduce to single stones. Quantum Go provides an interesting and tangible illustration of quantum concepts such as superposition, entanglement and collapse.

Alessandro Amabile, Maria Bondani, Immacolata De Simone +3 more

In this paper we introduce the new version of QTris, a board game designed to teach and learn Quantum Mechanics within the framework of Quantum Information and Computation. The key idea behind the game is that every game sequence simulates a process on a system of qubits. Thus, QTris can be effectively integrated as a pedagogical tool to teach Quantum Mechanics at high-school level following a two-state approach. After arguing in support of this latter approach, we describe QTris' basic rules and some of its possible extensions, emphasizing how the game mechanics puts in clear light key quantum concepts such as incompatibility, probabilistic measurement and unitary transformation. Moreover, we report on the results of a QTris-based educational activity which involved about 150 high-school students and provided encouraging preliminary indications that QTris can be a useful pedagogical platform to promote an immediate understanding of some key concepts of Quantum Mechanics.