Geometric phase-assisted single-parameter controlled phase compensation enabling quantum key distribution using phase-shifted Bell states

Entanglement-based quantum key distribution (QKD) relies on the distribution of high-fidelity maximally entangled Bell states, typically generated via spontaneous parametric down-conversion. Typically, unwanted relative phases arise from birefringence, pump-induced effects, imperfections in photon-pair generation, transmission through physical channels, and optical components, transforming Bell states into phase-shifted states. These phase errors degrade two-photon interference visibility, increase the quantum bit-error rate (QBER), and consequently reduce the secure key generation rate. Conventional compensation techniques, such as birefringent crystals, interferometric stabilization, and spatial light modulators, often involve trade-offs between complexity, loss, and implementation. Here, we demonstrate a single-parameter-controlled geometric-phase compensation scheme that can be implemented either at the source or the receiver to eliminate relative phases in Bell states arising from source imperfections or the birefringence of optical elements used in the experiment. We theoretically and experimentally establish the dependence of the QBER in the BBM92 protocol on the Bell-state relative phase and demonstrate that geometric-phase control effectively restores low-QBER operation by compensating phase errors. In a proof-of-concept experiment using a phase-shifted polarization Bell state, we achieve a state fidelity exceeding 95 \(\%\) and reduce the QBER below the 11 \(\%\) security threshold required for secure QKD. This work provides a simple, deterministic approach of Bell-state phase compensation, offering a practical phase-control module for future low-QBER entanglement-based quantum communication systems.