Parity-Based Time-Bin Encoding Enabling SWAP Between Polarization and Time-Bin Qubits

Abstract

Multi-degree-of-freedom photonic quantum processing requires routing between degree-of-freedom (DOF) qubit encodings on a single photon. A SWAP between polarization and time-bin qubits is Multi-degree-of-freedom photonic quantum processing requires routing between degree-of-freedom (DOF) qubit encodings on a single photon. A SWAP between polarization and time-bin qubits is an advantageous primitive for such architectures, however conventional early/late time-bin encoding does not support bidirectional logical time-bin flips from late to early which limits the ability to implement certain quantum operations. We introduce a parity-based time-bin encoding in which logical $|0{⟩}_T$ and $|1{⟩}_T$ correspond to even and odd multiples of a spacing $\hat{I}”t$, so that a physical delay of $\hat{I}”t$ implements $|0{⟩}_T\leftrightarrow |1{⟩}_T$. This encoding is the enabling ingredient that makes a polarization-controlled delay line implement ${\mathrm{CNOT}}_{P\to T}$ and aligns naturally with periodic refractive index modulation for ${\mathrm{CNOT}}_{T\to P}$. Composing three such CNOT operations sequentially results in a deterministic SWAP between polarization and time-bin degrees of freedom. We analyze field-based modulation polarization-rotation error probability and timing-resolution constraints set by both EOM drive electronics and photon detection.

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