Improved Key Rates for Quantum Key Distribution Employing Soft Metrics Using Bayesian Inference with Photon Counting Detectors

This paper investigates the potential improvements that may be obtained in terms of the secret key transmission rate in a Quantum Key Distribution (QKD) scheme whereby photon-counting detectors are used at the receiver. To take full advantage of such detectors, soft information is generated in the form of Log-Likelihood Ratios (LLRs) using a Bayesian estimator of phase of the signal pulse which is used to carry the information. The technique is general in a sense that any optical communication scheme whereby the received mean photon count is relatively small, but not necessarily below one and uses the polarization state of light to transmit the binary data may benefit from the soft information processing proposed, although in this paper, we have focused on the QKD application. We demonstrate using simulations the significant reduction in the residual Bit Error Rate (BER) and Frame Error Rate (FER) that is achievable using the proposed soft information processing scheme for a given Quantum BER (QBER) on the quantum link, after the information reconciliation process using LDPC Forward Error Correction (FEC) coding.