LDPC Coding for QKD at Higher Photon Flux Levels Based on Spatial Entanglement of Twin beams in PDC

Twin beams generated by Parametric Down Conversion (PDC) exhibit quantum correlations that has been effectively used as a tool for many applications including calibration of single photon detectors. By now, detection of multi-mode spatial correlations is a mature field and in principle, only depends on the transmission and detection efficiency of the devices and the channel. In [2, 4, 5], the authors utilized their know-how on almost perfect selection of modes of pairwise correlated entangled beams and the optimization of the noise reduction to below the shot-noise level, for absolute calibration of Charge Coupled Device (CCD) cameras. The same basic principle is currently being considered by the same authors for possible use in Quantum Key Distribution (QKD) [3, 1]. The main advantage in such an approach would be the ability to work with much higher photon fluxes than that of a single photon regime that is theoretically required for discrete variable QKD applications (in practice, very weak laser pulses with mean photon count below one are used).The natural setup of quantization of CCD detection area and subsequent measurement of the correlation statistic needed to detect the presence of the eavesdropper Eve, leads to a QKD channel model that is a Discrete Memoryless Channel (DMC) with a number of inputs and outputs that can be more than two (i.e., the channel is a multi-level DMC). This paper investigates the use of Low Density Parity Check (LDPC) codes for information reconciliation on the effective parallel channels associated with the multi-level DMC. The performance of such codes are shown to be close to the theoretical limits.