Decoherence-controlled collective criticality in a two-dimensional quantum Stag Hunt
Abstract
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 Q=iℤ and D=i𝕐, noisy two-player payoff matrices are determined for phase damping, depolarization, and amplitude damping and mapped exactly to channel dependent Ising parameters J(Γ,p) and H(Γ,p). Phase damping and depolarization show the clearest contrast: they share the same microscopic neutrality branch 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*≈ 0.233460…, 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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BibTeX
@misc{tah2026decoherencecontrolled,
title = {{Decoherence-controlled collective criticality in a two-dimensional quantum Stag Hunt}},
author = {Rajdeep Tah},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.02957},
eprint = {2609.02957},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02957},
}
RIS
TY - UNPB
TI - Decoherence-controlled collective criticality in a two-dimensional quantum Stag Hunt
AU - Rajdeep Tah
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.02957
UR - https://arxiv.org/abs/2609.02957
AB - 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 Q=iℤ and D=i𝕐, noisy two-player payoff matrices are determined for phase damping, depolarization, and amplitude damping and mapped exactly to channel dependent Ising parameters J(Γ,p) and H(Γ,p). Phase damping and depolarization show the clearest contrast: they share the same microscopic neutrality branch 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_*≈ 0.233460…, 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.
ER -