二维量子 stag hunt 中退相干控制的集体临界性
Decoherence-controlled collective criticality in a two-dimensional quantum Stag Hunt
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- Florida State University（佛罗里达州立大学）
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中文总结 AI 辅助
本研究针对嵌入正方形晶格的 EWL stag hunt 博弈，探究不同退相干通道对其微观策略中性条件及集体临界性的影响，发现退极化可驱动二维伊辛临界点，而相位阻尼、振幅阻尼表现出不同特性。
中文摘要 AI 辅助
物理退相干可在保留量子博弈微观策略中性条件的同时，改变对应相互作用群体的热力学 regime。我们对嵌入正方形晶格最近邻独立对局的 Eisert-Wilkens-Lewenstein（EWL） stag hunt 博弈开展研究，针对受限策略 Q=iℤ 和 D=i𝕐，确定了相位阻尼、退极化和振幅阻尼下的含噪两人收益矩阵，并精确映射为依赖通道的伊辛参数 𝔍(Γ,p) 和 ℌ(Γ,p)。相位阻尼与退极化表现出最显著的对比：二者共享相同的微观中性分支 ℌ=0，且仅退极化会以 (1-p)² 的形式抑制相互作用。在 β=1 时，这产生了退极化驱动的正方形晶格临界点 p*≈0.233460…，而相位阻尼沿同一中性分支保持在有序共存 regime。蒙特卡洛有限尺寸标度与二维伊辛临界性一致，区分了 p* 以下场驱动的共存与 p* 以上的平滑交叉。振幅阻尼还显示出对通道位置的强依赖性：策略后中性分支在 p=1/3 处达到 Γ=0，随后消失。资源负性进一步表明，微观两量子比特纠缠与集体相互作用强度是不同的量，所得扩展晶格仍为普通经典伊辛系统。
英文摘要
Physical decoherence can preserve the microscopic strategic neutrality (i.e. zero effective field and equal potential of the two homogeneous strategic orientations) of a quantum game while changing the thermodynamic regime of the corresponding interacting population. We demonstrate this for an Eisert--Wilkens--Lewenstein (\textit{EWL}) Stag Hunt embedded as independent nearest neighbor encounters on a square lattice. For the restricted strategies $\mathsf{Q}=i\mathbb{Z}$ and $\mathsf{D}=i\mathbb{Y}$, noisy two-player payoff matrices are determined for phase damping, depolarization, and amplitude damping and mapped exactly to channel dependent Ising parameters $\mathfrak{J}(Γ,p)$ and $\mathfrak{H}(Γ,p)$. Phase damping and depolarization show the clearest contrast: they share the same microscopic neutrality branch $\mathfrak{H}=0$, while only depolarization suppresses the interaction as $(1-p)^2$. At $β=1$, this produces an exact depolarization-driven square-lattice critical point at $p_{*}\approx 0.233460\ldots$, whereas phase damping remains in the ordered coexistence regime along the same neutrality branch. Monte Carlo finite size scaling is consistent with two-dimensional Ising criticality and distinguishes field driven coexistence below $p_{*}$ from a smooth crossover above it. Amplitude damping additionally reveals a strong dependence on channel placement: the post-strategy neutrality branch reaches $Γ=0$ at $p=1/3$ and then disappears. Resource negativity further shows that microscopic two-qubit entanglement and collective interaction strength are distinct quantities. The resulting extended lattice remains an ordinary classical Ising system.
