Finite-key security analysis of quantum key distribution with imperfect light sources

Abstract

In recent years, the gap between theory and practice in quantum key\ndistribution (QKD) has been significantly narrowed, particularly for QKD\nsystems with arbitrarily awed optical receivers. The status for QKD systems\nwith imperfect light sources is however less satisfactory, in the sense that\nthe resulting secure key rates are often overly-dependent on the quality of\nstate preparation. This is especially the case when the channel loss is high.\nVery recently, to overcome this limitation, Tamaki et al proposed a QKD\nprotocol based on the so-called rejected data analysis, and showed that its\nsecurity|in the limit of infinitely long keys|is almost independent of any\nencoding flaw in the qubit space, being this protocol compatible with the decoy\nstate method. Here, as a step towards practical QKD, we show that a similar\nconclusion is reached in the finite-key regime, even when the intensity of the\nlight source is unstable. More concretely, we derive security bounds for a wide\nclass of realistic light sources and show that the bounds are also efficient in\nthe presence of high channel loss. Our results strongly suggest the feasibility\nof long distance provably-secure communication with imperfect light sources.\n