Nash Equilibrium from Quantum-Field Entanglement
Abstract
Entanglement harvesting transfers quantum field correlations to localized probes, yet whether these correlations can alter stable strategic behavior has remained unclear. We formulate a quantum-input game in which two Unruh-DeWitt detectors harvest vacuum entanglement from a free massless scalar field in (3+1)-dimensional Minkowski spacetime. A referee converts this state into payoffs using independent question qubits and phase-calibrated local Bell measurements. To leading perturbative order, the mean reward is proportional to the signed entanglement margin √(ℋ2+𝒬2)−𝒫, where ℋ is the Hadamard correlation contribution, 𝒬 is the Pauli-Jordan causal contribution, and 𝒫 is the local excitation noise. Away from payoff degeneracies, allowing each player to exit or to choose an early or late interaction yields 1+2n+ trembling-hand perfect equilibria, where n+ counts the positive-reward timing equilibria. For one fixed protocol, five analytically certified settings realize the sequence 7→3→1→7→1. They represent the spacelike region, the first commutator lobe, central carrier cancellation, the second lobe, and the post-wavefront Huygens regime. Thus, within this fixed quantum-input verification protocol, distinct field-correlation regimes generate different stable strategic structures.
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BibTeX
@misc{xu2026nash,
title = {{Nash Equilibrium from Quantum-Field Entanglement}},
author = {Hao Xu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33188},
eprint = {2609.33188},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33188},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nash Equilibrium from Quantum-Field Entanglement
AU - Hao Xu
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33188
UR - https://arxiv.org/abs/2609.33188
AB - Entanglement harvesting transfers quantum field correlations to localized probes, yet whether these correlations can alter stable strategic behavior has remained unclear. We formulate a quantum-input game in which two Unruh-DeWitt detectors harvest vacuum entanglement from a free massless scalar field in (3+1)-dimensional Minkowski spacetime. A referee converts this state into payoffs using independent question qubits and phase-calibrated local Bell measurements. To leading perturbative order, the mean reward is proportional to the signed entanglement margin √(ℋ^2+𝒬^2)−𝒫, where ℋ is the Hadamard correlation contribution, 𝒬 is the Pauli-Jordan causal contribution, and 𝒫 is the local excitation noise. Away from payoff degeneracies, allowing each player to exit or to choose an early or late interaction yields 1+2n_+ trembling-hand perfect equilibria, where n_+ counts the positive-reward timing equilibria. For one fixed protocol, five analytically certified settings realize the sequence 7→3→1→7→1. They represent the spacelike region, the first commutator lobe, central carrier cancellation, the second lobe, and the post-wavefront Huygens regime. Thus, within this fixed quantum-input verification protocol, distinct field-correlation regimes generate different stable strategic structures.
ER -