  The competitive multi-armed bandit (CMAB) problem is related to social issues
such as maximizing total social benefits while preserving equality among
individuals by overcoming conflicts between individual decisions, which could
seriously decrease social benefits. The study described herein provides
experimental evidence that entangled photons physically resolve the CMAB in the
2-arms 2-players case, maximizing the social rewards while ensuring equality.
Moreover, we demonstrated that deception, or outperforming the other player by
receiving a greater reward, cannot be accomplished in a
polarization-entangled-photon-based system, while deception is achievable in
systems based on classical polarization-correlated photons with fixed
polarizations. Besides, random polarization-correlated photons have been
studied numerically and shown to ensure equality between players and deception
prevention as well, although the CMAB maximum performance is reduced as
compared with entangled photon experiments. Autonomous alignment schemes for
polarization bases were also experimentally demonstrated based only on decision
conflict information observed by an individual without communications between
players. This study paves a way for collective decision making in uncertain
dynamically changing environments based on entangled quantum states, a crucial
step toward utilizing quantum systems for intelligent functionalities.
