  As quantum processors advance, the emergence of large-scale decentralized
systems involving interacting quantum-enabled agents is on the horizon. Recent
research efforts have explored quantum versions of Nash and correlated
equilibria as solution concepts of strategic quantum interactions, but these
approaches did not directly connect to decentralized adaptive setups where
agents possess limited information. This paper delves into the dynamics of
quantum-enabled agents within decentralized systems that employ no-regret
algorithms to update their behaviors over time. Specifically, we investigate
two-player quantum zero-sum games and polymatrix quantum zero-sum games,
showing that no-regret algorithms converge to separable quantum Nash equilibria
in time-average. In the case of general multi-player quantum games, our work
leads to a novel solution concept, (separable) quantum coarse correlated
equilibria (QCCE), as the convergent outcome of the time-averaged behavior
no-regret algorithms, offering a natural solution concept for decentralized
quantum systems. Finally, we show that computing QCCEs can be formulated as a
semidefinite program and establish the existence of entangled (i.e.,
non-separable) QCCEs, which cannot be approached via the current paradigm of
no-regret learning.
