Parity-Based Time-Bin Encoding Enabling SWAP Between Polarization and Time-Bin Qubits
The work introduces a parity-based time-bin encoding for single photons to enable deterministic swapping between polarization and time-bin qubits. This encoding maps logical states to even or odd multiples of a time spacing, allowing a physical delay of one spacing ($\Delta t$) to flip the logical time bin. This enables standard quantum gates like CNOTs, which compose into a full SWAP gate for routing degrees of freedom on a single photon.