  The emergence of quantum technologies is heating up the debate on quantum
supremacy, usually focusing on the feasibility of looking good on paper
algorithms in realistic settings, due to the vulnerability of quantum systems
to myriad sources of noise. In this vein, an interesting example of quantum
pseudo-telepathy games that quantum mechanical resources can theoretically
outperform classical resources is the Magic Square game (MSG), in which two
players play against a referee. Due to noise, however, the unit winning
probability of the players can drop well below the classical limit. Here, we
propose a timely and unprecedented experimental setup for quantum computation
with quantum dots inside optical cavities, along with ancillary photons for
realizing interactions between distant dots to implement the MSG. Considering
various physical imperfections of our setup, we first show that the MSG can be
implemented with the current technology, outperforming the classical resources
under realistic conditions. Next, we show that our work gives rise to a new
version of the game. That is, if the referee has information on the physical
realization and strategy of the players, he can bias the game through filtered
randomness and increase his winning probability. We believe our work
contributes to not only quantum game theory, but also quantum computing with
quantum dots.
