ABSTRACT The geometric phase, arising from the cyclic/non‐cyclic evolution of a polarization state of light, is typically measured using interferometric methods that often introduce unwanted dynamic phase contributions. Here, we present a phase measurement technique based on the quantum correlation of pair photons to measure the geometric phase of a classical beam without any dynamic phase contribution. The transfer of the geometric phase of the classical pump beam onto polarization‐entangled pair photons generated via spontaneous parametric down‐conversion in a Sagnac interferometer scheme enables easy control over the quantum state. Characterization of the quantum states reveals that the geometric phase of the pump beam controls the coincidence counts, entanglement visibility, Bell's parameter, quantum‐state tomography, and fidelity, in close agreement with theoretical predictions. We observe sinusoidal modulation of Bell's parameter and state fidelity with changes in the geometric phase, resulting in transitions between orthogonal Bell states and Bell‐like maximally entangled states. Our results establish the geometric phase of the classical pump as a tunable parameter for quantum state control, offering a compact, passive platform for phase manipulation in quantum photonic systems, enabling geometric‐phase‐controlled quantum operations, and compensating for the unwanted phase acquired by the quantum state during propagation.
ABSTRACT The geometric phase, arising from the cyclic/non‐cyclic evolution of a polarization state of light, is typically measured using interferometric methods that often introduce unwanted dynamic phase contributions. Here, we present a phase measurement technique based on the quantum correlation of pair photons to measure the geometric phase of a classical beam without any dynamic phase contribution. The transfer of the geometric phase of the classical pump beam onto polarization‐entangled pair photons generated via spontaneous parametric down‐conversion in a Sagnac interferometer scheme enables easy control over the quantum state. Characterization of the quantum states reveals that the geometric phase of the pump beam controls the coincidence counts, entanglement visibility, Bell's parameter, quantum‐state tomography, and fidelity, in close agreement with theoretical predictions. We observe sinusoidal modulation of Bell's parameter and state fidelity with changes in the geometric phase, resulting in transitions between orthogonal Bell states and Bell‐like maximally entangled states. Our results establish the geometric phase of the classical pump as a tunable parameter for quantum state control, offering a compact, passive platform for phase manipulation in quantum photonic systems, enabling geometric‐phase‐controlled quantum operations, and compensating for the unwanted phase acquired by the quantum state during propagation.
The geometric phase, originating from the cyclic evolution of a state, such as polarization on the Poincaré sphere, is typically measured through interferometric approaches that often include unwanted contributions from the dynamic phase. Here, we present a non-interferometric technique based on quantum correlation of pair photons to measure the geometric phase of a classical beam. The transfer of geometric phase of the classical pump beam arising from the cyclic evolution of its polarization state on the Poincaré sphere onto the polarization-entangled pair photons generated via spontaneous parametric down-conversion in a Sagnac interferometer enables easy control over the quantum state. Characterization of the generated quantum states reveals that the geometric phase of the pump beam controls the coincidence counts, entanglement visibility, Bell's parameter, quantum state tomography, and fidelity in close agreement with theoretical predictions. We observe sinusoidal modulation of the Bell's parameter and state fidelity with changes in the geometric phase, resulting in transitions between orthogonal Bell states and Bell-like maximally entangled states. Our results establish the geometric phase of the classical pump as a tunable parameter for quantum state control, offering a compact, passive platform for phase manipulation in quantum photonic systems, enabling geometric phase-based quantum gates, and compensating unwanted phase acquired by the quantum state on propagation.
Abstract Entanglement-based quantum key distribution (QKD) relies on the distribution of high-fidelity maximally entangled Bell states, typically generated via spontaneous parametric down-conversion (SPDC). In practical systems, unwanted relative phases arise from birefringence, pump-beam contributions, imperfect photon-pair generation, transmission through physical channels, and collection, transforming Bell states into phase-shifted states. This degrades interference visibility, increases the quantum bit error rate (QBER), and limits secure key generation. Conventional compensation techniques, such as birefringent crystals, interferometric stabilization, and spatial light modulators, are often impractical in real-world deployments. Here, we demonstrate a simple and versatile phase-compensation scheme that can be implemented at either the source or the receiver to eliminate arbitrary relative phases in Bell states. We theoretically and experimentally quantify the dependence of QBER in the BBM92 protocol on the relative phase and show that geometric-phase-based control can effectively restore entanglement quality. In a proof-of-concept experiment using a nondegenerate polarization Bell state, we achieve a fidelity exceeding 95% and reduce QBER below the 11% security threshold required for secure QKD. This robust approach enables practical phase control in entangled-photon systems and can be extended to time-bin QKD via time–polarization mapping, offering a promising route toward stable, low-QBER quantum communication.
Entanglement-based quantum key distribution (QKD) relies on the distribution of high-fidelity maximally entangled Bell states, typically generated via spontaneous parametric down-conversion (SPDC). In practical systems, unwanted relative phases arise from birefringence, pump-beam contributions, imperfect photon-pair generation, transmission through physical channels, and collection, transforming Bell states into phase-shifted states. This degrades interference visibility, increases the quantum bit error rate (QBER), and limits secure key generation. Conventional compensation techniques, such as birefringent crystals, interferometric stabilization, and spatial light modulators, are often impractical in real-world deployments. Here, we demonstrate a simple and versatile phase-compensation scheme that can be implemented at either the source or the receiver to eliminate arbitrary relative phases in Bell states. We theoretically and experimentally quantify the dependence of QBER in the BBM92 protocol on the relative phase and show that geometric-phase-based control can effectively restore entanglement quality. In a proof-of-concept experiment using a nondegenerate polarization Bell state, we achieve a fidelity exceeding 95% and reduce QBER below the 11% security threshold required for secure QKD. This robust approach enables practical phase control in entangled-photon systems and can be extended to time-bin QKD via time-polarization mapping, offering a promising route toward stable, low-QBER quantum communication.
The wave function of a quantum system may acquire an additional phase factor (the geometric phase), when its parameters undergo a cyclic change. An optical manifestation of the geometric phase is the change in the phase of a light wave produced when its state of polarization is taken around a circuit on the Poincare sphere. This phase change can be verified by interferometric measurements. We describe an interferometer in which the two beams traverse the same path in opposite directions, so that their optical paths are always equal, and the phase difference between them is varied by operating on the geometric phase. Measurements made with this interferometer, at a light level at which the probability of more than one photon being present simultaneously in the interferometer was negligibly small, confirmed that the interference effects observed due to the geometric phase persist down to the single photon level.
We present a novel interferometric arrangement that makes it possible to measure with great versatility geometric phases produced in polarization states of classical light. Our arrangement is robust against thermal and mechanical disturbances and can be set up in a Mach-Zehnder, a Michelson or a Sagnac configuration. We present results concerning the geometric phase as an extension of previous measurements of the Pancharatnam, or total phase. The geometric phase is obtained by compensating the dynamical contribution to the total phase, so as to extract out of it a purely geometric phase. This can be achieved over trajectories on the Poincare sphere that are not necessarily restricted to be great circles (geodesics). We thus demonstrate the feasibility of our method for dynamical extraction of the geometric contribution to the total phase, a prerequisite for building geometric quantum gates. Although our results correspond to polarization states of classical light, the same methodology could be applied in the case of polarization states of single photons.
In this work we performed two experiments to observe the fractional topological phases in two qudits photonic systems. The qudits are encoded in the transverse position degree of freedom of photon pairs generated by the spontaneous parametric down conversion after being transmitted through multiple slits. The photons in this phenomenon are quantum correlated in momentum and energy. Initially we review the theory about the origin of the phases acquired by the evolving quantum states of one and two qubits, where we identify the dynamic, the geometric and the topological phases. Then we examine the generalization of topological phases for two qudits, and discuss its relation with the concept of connectedness of a space. Next we show a way to measure the topological phase, considering that it must appear as a relative phase between two interfering quantum states. To realize the measurement we build an optical interferometer with a spatial light modulator inside it to implement the necessary unitary operations. The polarization is used as an auxiliary degree of freedom for the operations to act conditionally. The results are close to the theoretical predictions, showing the dependence of the phase with the Hilbert space dimension of the state. In a second setup we measure the topological phase for qudits without using a longitudinal interferometer. A new source of polarization entangled photon pairs is used in this new setup. The entanglement in the auxiliary degree of freedom, polarization, is used as a resource to eliminate the interferometer, propitiating a significant improvement in the visibility of the measured interference curves, and a large increase in the signal to noise ratio. In this new setup, we are also capable of realize the unitary operations in both parts of the two qubit system.