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.

翻译：随着量子处理器的进步，涉及量子智能体相互作用的大规模去中心化系统即将出现。近期研究探索了量子版本的纳什均衡和相关均衡作为战略量子交互的解概念，但这些方法并未直接关联到智能体信息有限的去中心化自适应设置。本文深入研究了去中心化系统中采用无遗憾算法随时间更新其行为的量子智能体的动力学。具体而言，我们研究了双人量子零和博弈与多矩阵量子零和博弈，表明无遗憾算法在时间平均意义上收敛于可分离量子纳什均衡。对于一般多人量子博弈，我们的工作提出了一种新解概念——（可分离）量子粗相关均衡（QCCE），作为无遗憾算法时间平均行为的收敛结果，为去中心化量子系统提供了自然的解概念。最后，我们证明QCCE的计算可表述为半定规划问题，并确立了纠缠（即不可分离）QCCE的存在性，这类均衡无法通过当前的无遗憾学习范式逼近。