Decoherence-controlled collective criticality in a two-dimensional quantum Stag Hunt

Abstract:Physical decoherence can preserve the microscopic strategic neutrality condition 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 $\mathfrak{J}(\Gamma,p)$ and $\mathfrak{H}(\Gamma,p)$. 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 $\beta=1$, 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 $\Gamma=0$ 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.

Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Computational Physics (physics.comp-ph); Quantum Physics (quant-ph)

arXiv:2609.02957 [cond-mat.stat-mech]

(or arXiv:2609.02957v1 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2609.02957 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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