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In recent years, the gap between theory and practice in quantum keydistribution (QKD) has been significantly narrowed, particularly for QKDsystems with arbitrarily awed optical receivers. The status for QKD systemswith imperfect light sources is however less satisfactory, in the sense thatthe resulting secure key rates are often overly-dependent on the quality ofstate preparation. This is especially the case when the channel loss is high.Very recently, to overcome this limitation, Tamaki et al proposed a QKDprotocol based on the so-called rejected data analysis, and showed that itssecurity|in the limit of infinitely long keys|is almost independent of anyencoding flaw in the qubit space, being this protocol compatible with the decoystate method. Here, as a step towards practical QKD, we show that a similarconclusion is reached in the finite-key regime, even when the intensity of thelight source is unstable. More concretely, we derive security bounds for a wideclass of realistic light sources and show that the bounds are also efficient inthe presence of high channel loss. Our results strongly suggest the feasibilityof long distance provably-secure communication with imperfect light sources.

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