Time-Entanglement QKD: Secret Key Rates and Information Reconciliation Coding

In time entanglement-based quantum key distribution (TE-QKD), Alice and Bob extract the raw key bits from the arrival times of entangled photon pairs. Each entangled pair can contribute to multiple key bits depending on how precisely Alice and Bob can measure the photon arrival times. Thus, TE-QKD can potentially increase the secret key rate compared to typical QKD implementations, which extract up to a bit per photon. Because of entanglement, the times of photon arrivals at Alice's and Bob's detectors and, thus, their raw keys should be identical. However, practical photon detectors suffer from time jitter errors. These errors cause discrepancies between Alice's and Bob's raw keys. Therefore, Alice must send information to Bob through the public channel to reconcile their raw keys. The amount of data sent for reconciliation represents a loss, rendering secret keys shorter than the raw keys. We compute the secret key rates possible in systems with detector jitter errors and show that they are much higher than those achievable in polarization entanglement-based QKD. We then construct codes for information reconciliation to approach these rates. We demonstrate that short and moderate-length standard error-correcting codes represent excellent information reconciliation choices, making TE-QKD a promising technology.