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Distinguishing Geometric Phase from Intrinsic Rotation of Correlation Axes in Entangled States

Runbiao Fang

Published Jan 1, 2026• 0 citations
Publisher

Abstract

This work investigates the distinction between the geometric phase and the intrinsic rotation of correlation axes in entangled photon states. Motivated by recent experiments observing phase shifts due to Earth's rotation, we analyze two competing physical hypotheses: the "Geometric Phase" hypothesis (where correlation axes are fixed to the inertial frame) and the "Intrinsic Rotation" hypothesis (where axes rotate with the laboratory). We demonstrate that standard Sagnac phase measurements cannot distinguish between these scenarios. Therefore, we propose a novel, experimentally verifiable criterion based on the visibility dependence on the accumulated rotation angle to resolve this fundamental question.

DOI
10.5281/zenodo.20329123

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This work investigates the distinction between the geometric phase and the intrinsic rotation of correlation axes in entangled photon states. Motivated by recent experiments observing phase shifts due to Earth's rotation, we analyze two competing physical hypotheses: the "Geometric Phase" hypothesis (where correlation axes are fixed to the inertial frame) and the "Intrinsic Rotation" hypothesis (where axes rotate with the laboratory). We demonstrate that standard Sagnac phase measurements cannot distinguish between these scenarios. Therefore, we propose a novel, experimentally verifiable criterion based on the visibility dependence on the accumulated rotation angle to resolve this fundamental question.
We show the targeted phase-manipulation of an entangled photonic Bell state via non-inertial motion. To this end, we place a very compact laboratory, consisting of a SPDC source and a Sagnac interferometer, on a rotating platform (non-inertial reference frame). The photon pairs of a ∣ϕ⟩\ketϕ∣ϕ⟩-state are in a superposition of co- and counter-rotation. The phase of the ∣ϕ⟩\ketϕ∣ϕ⟩-state is linearly dependent on the angular velocity of the rotating platform due to the Sagnac effect. We measure the visibility and certify entanglement with the Bell-CHSH parameter SSS. Additionally, we conduct a partial quantum state tomography on the Bell states in a non-inertial environment. Our experiment showcases the unitary transformation of an entangled state via non-inertial motion and constitutes not only a switch between a ∣ϕ−⟩\ket{ϕ^{-}}∣ϕ−⟩-state and a ∣ϕ+⟩\ket{ϕ^{+}}∣ϕ+⟩-state but also a further experiment at the interplay of non-inertial motion and quantum physics.
Abstract Quantum entanglement is commonly described as a nonlocal correlation between spatially separated systems, raising foundational questions regarding its physical interpretation. In this work, a phenomenological framework is presented in which entanglement is interpreted geometrically as arising from a shared spatial phase structure established during state preparation. The approach proposes that rotational dynamics may generate a sinusoidal radial spatial organization (“radial waves”) that provides correlated geometric conditions at the moment of formation of an entangled state. Within this interpretation, the correlations observed in measurement outcomes reflect this shared phase geometry rather than any superluminal interaction or information transfer occurring after separation. The framework does not modify the standard quantum mechanical formalism and reproduces the familiar cosine correlation structure characteristic of Bell-type experiments. The formulation emphasizes internal geometric consistency and dimensional coherence while leaving established quantum predictions unchanged. A representative illustrative case is presented to demonstrate internal consistency, while broader applications and experimental considerations are deferred to subsequent work.
Einstein's theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle's intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin's coupling with the angular velocity of a rotating magnetic field. This coupling is a purely quantum mechanical extension of the Sagnac effect. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree with the predictions derived from the Pauli-Schrodinger equation.
Quantum entanglement is traditionally described as a statistical correlation encoded in a many-body wavefunction. While this framework successfully predicts measurement outcomes, it leaves unresolved whether entanglement reflects purely probabilistic structure or an intrinsic physical organization of quantum states. Recent experiments have demonstrated that high-dimensional entangled states possess thousands of distinct, experimentally accessible topological invariants that persist under basis changes, noise, and local perturbations. These features are difficult to reconcile with a purely statistical interpretation of the wavefunction, but arise naturally if entanglement corresponds to intrinsic geometric structure within state space. This work analyzes experimental results reported in Nature Communications (2025) showing robust, high-dimensional topological structure embedded in conventional entangled states. We show that the multiplicity, stability, and basis-independence of these invariants support an interpretation of entanglement as intrinsic geometry rather than as observer-dependent probability. Under this interpretation, nonlocal correlations reflect shared geometric structure rather than information transfer, and robustness arises from topological protection rather than statistical averaging. The paper does not modify the formal machinery of quantum mechanics, but reframes the physical meaning of the quantum state. Entanglement is interpreted as a geometric configuration of collective modes whose topology constrains allowed correlations. This perspective provides a natural physical explanation for robustness, nonlocality, and measurement independence, and places strong constraints on interpretations in which the wavefunction is purely epistemic. Together with independent results in condensed matter and gravitational physics, these findings support a geometry-first interpretation of quantum phenomena and contribute to a growing body of experimental evidence that quantum states possess intrinsic physical structure beyond probabilistic description.
The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. [Phys. Rev. A 69, 032112 (2004)] and expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, has been observed for a spin-path-entangled neutron state in an interferometric setup. It is experimentally demonstrated that the effect of geometric phase can be balanced by a change in Bell angles. The geometric phase is acquired during a time-dependent interaction with a radiofrequency field. Two schemes, polar and azimuthal adjustment of the Bell angles, are realized and analyzed in detail. The former scheme yields a sinusoidal oscillation of the correlation function SSS, dependent on the geometric phase, such that it varies in the range between 222 and 222\sqrt{2}22​ and therefore always exceeds the boundary value 222 between quantum mechanic and noncontextual theories. The latter scheme results in a constant, maximal violation of the Bell-like CHSH inequality, where SSS remains 222\sqrt{2}22​ for all settings of the geometric phase.