Geometric Entangling Gates Without Interaction: A Unified Effective Action Approach to Path-Identity Entanglement

Medina Albarenga, JUAN AlBERTO

Published Nov 23, 2025• 0 citations

Abstract

Recent experiments have demonstrated that two distant photons can become entangled even when they originate from independent sources and never interact nor share a traditional Bell-state measurement. This class of experiments—known as entanglement by path identity (Wang et al., 2024; Krenn et al., 2017)—reveals a mode of entanglement generation fundamentally different from the usual interactionbased or measurement-induced protocols. This work develops a fully geometric formulation of such effects using a Unified Effective Average Action (UEAA), originally introduced in the context of the Integrated Geometric Model with Renormalization Group (IGM–RG). The UEAA provides a natural language to describe optical modes, path indistinguishability, and nonlocal correlations via a bilocal kernel constrained by a geometric exclusion principle (GEP). The paper constructs a minimal UEAA for two remote optical modes, derives an entanglement curvature scalar from the bilocal kernel, and shows that this curvature is a monotonic entanglement measure equivalent to concurrence in the single-excitation subspace. As a consequence, the path-identity experiments are interpreted as the activation of a geometric mode of the quantum state, rather than as a mysterious 1nonlocal interaction. This formalism suggests a new paradigm of geometric quantum computing, where entangling gates are implemented through global geometric constraints rather than physical interaction. The results unify quantum optics, quantum information, and geometric field theory within a single effective-action framework and open a pathway toward novel architectures for distributed quantum networks.

DOI: 10.5281/zenodo.17686457

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