Quantum games: Taking advantage of quantum effects to attain a winning edge

Şahin Kaya Özdemir, Junichi Shimamura, Nobuyuki Imoto

Indranil Chakrabarty

In this work we have introduced two party pseudo telepathy games with respective winning conditions. One cannot win these games deterministically by any kind of classical protocols. Interestingly we find out that in quantum world, these winning conditions can be achieved if the players share an entangled state. We also introduced a game which is impossible to win if the players are form classical world, (both probabilistically and deterministically) yet there exists a perfect quantum strategy by following which, one can attain the winning condition of the game.

Jiangfeng Du, Xiaodong Xu, Hui Li +2 more

J N Leaw, S A Cheong

In this paper, we perform a minimalistic quantization of the classical game of tic-tac-toe, by allowing superpositions of classical moves. In order for the quantum game to reduce properly to the classical game, we require legal quantum moves to be orthogonal to all previous moves. We also admit interference effects, by squaring the sum of amplitudes over all moves by a player to compute his or her occupation level of a given site. A player wins when the sum of occupations along any of the eight straight lines we can draw in the 3 × 3 grid is greater than or equal to 3. We play the quantum tic-tac-toe first randomly, and then deterministically, to explore the impact different opening moves, end games and different combinations of offensive and defensive strategies have on the outcome of the game. In contrast to the classical tic-tac-toe, the deterministic quantum game does not always end in a draw. In contrast also to most classical two-player games of no chance, it is possible for player 2 to win. More interestingly, we find that player 1 enjoys an overwhelming quantum advantage when he opens with a quantum move, but loses this advantage when he opens with a classical move. We also find the quantum blocking move, which consists of a weighted superposition of moves that the opponent could use to win the game, to be very effective in denying the opponent his or her victory. We then speculate what implications these results might have on quantum information transfer and portfolio optimization.

Giannicola Scarpa

Xavier Coiteux-Roy, Stefan Wolf

The CHSH no-signalling game studies Bell nonlocality by showcasing a gap between the win rates of classical strategies, quantum-entangled strategies, and no-signalling strategies. Similarly, the CHSH* single-system game explores the advantage of irreversible processes by showcasing a gap between the win rates of classical reversible strategies, quantum reversible strategies, and irreversible strategies. The irreversible process of erasure rules supreme for the CHSH* single-system game, but this erasure advantage does not necessarily extend to every single-system game: We introduce the 32-Game, in which reversibility is irrelevant and only the distinction between classical and quantum operations matters. We showcase our new insight by modifying the CHSH* game to make it erasure-immune, while conserving its quantum advantage. We conclude by the reverse procedure: We tune the 32-Game to make it erasure-vulnerable, and erase its quantum advantage in the process. The take-home message is that, when the size of the single-system is too small for Alice to encode her whole input, quantum advantage and erasure advantage can happen independently.