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The emergence of quantum technologies is heating up the debate on quantumsupremacy, usually focusing on the feasibility of looking good on paperalgorithms in realistic settings, due to the vulnerability of quantum systemsto myriad sources of noise. In this vein, an interesting example of quantumpseudo-telepathy games that quantum mechanical resources can theoreticallyoutperform classical resources is the Magic Square game (MSG), in which twoplayers play against a referee. Due to noise, however, the unit winningprobability of the players can drop well below the classical limit. Here, wepropose a timely and unprecedented experimental setup for quantum computationwith quantum dots inside optical cavities, along with ancillary photons forrealizing interactions between distant dots to implement the MSG. Consideringvarious physical imperfections of our setup, we first show that the MSG can beimplemented with the current technology, outperforming the classical resourcesunder realistic conditions. Next, we show that our work gives rise to a newversion of the game. That is, if the referee has information on the physicalrealization and strategy of the players, he can bias the game through filteredrandomness and increase his winning probability. We believe our workcontributes to not only quantum game theory, but also quantum computing withquantum dots.

Surpassing the Classical Limit in Magic Square Game with Distant Quantum Dots Coupled to Optical Cavities