Quantum pseudo-telepathy in spin systems: the magic square game under magnetic fields and the Dzyaloshinskii–Moriya interaction

Abstract

The Dzyaloshinskii–Moriya (DM) interaction has been proved to excite entanglement of spin systems, enhancing the ability to realizing various quantum tasks such as teleportation. In this work we consider DM interaction—to the best of our knowledge for the first time—in quantum game theory. We study the winning probability of the magic square game played with the thermally entangled state of spin models under external magnetic fields and DM interaction. We analytically show that although DM interaction excites the entanglement of the system as expected, it surprisingly reduces the winning probability of the game, acting like temperature or magnetic fields, and also show that the effects of DM interaction and an inhomogeneous magnetic field on the winning probability are identical. In addition, we show that the XXZ model is considerably more robust than the XX model against destructive effects. Our results open up new insights for quantum information processing with spin systems.