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

• URL: http://arxiv.org/abs/2609.02957v1
• Date: Wed, 02 Sep 2026 04:20:17 GMT
• Title: Decoherence-controlled collective criticality in a two-dimensional quantum Stag Hunt
• Abstract summary: Physical decoherence can preserve the microscopic strategic neutrality condition of a quantum game.<n>We demonstrate this for an Eisert--Wilkens--Lewenstein (textitEWL) Stag Hunt embedded as independent nearest neighbor encounters on a square lattice.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\mathfrak{J}(Γ,p)$ 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.

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