Two way quantum key distribution in imperfect settings

Abstract

This thesis studies the security and performance of a two-way quantum key distribution protocol namely LM05 given imperfect settings. A toy model for such a two-way protocol; i.e. a model protocol which essentially mimics the LM05 was proposed in which in some sense, it would distill only the most essential features of a two-way QKD scheme and inherently simplify its security analysis with regards to the intercept / resend, two dimensional ancilla based attack and photon number splitting attack. A simple but relevant theorem was proven and noting the obvious advantage of such a model in allowing for single as well as double photon contributions, appropriate key rate formula was derived. It was shown that given an imperfect photon source we had to resort to consider Eve’s Renyi information gain for the double photon contribution case. The results exhibit a favorable light on ToM in comparisons against BB84 which highlights an important feature of two-way schemes, i.e. the inclusion of double photon contributions play a very significant role in key generation and allows for a higher key rate compared to BB84 despite the relatively extreme toll of lossy channels. A sufficient condition for ToM’s advantage over BB84 was derived and noted that the ultimate culprit seems to be the transmitivity of Alice’s equipments. The possible application of the decoy state method on LM05 scheme was also studied in order to learn the effects on the distance ad key rate. Also considering both the case contributions of single and double photon pulses, relevant lower bounds on the corresponding gains in a practical decoy state implementation using two intensities for decoy states were derived. Two different approaches were used in deriving the key rate formulas and several considerations on the derivations of the bounds were made for comparison. Given the results of comparing these with an ideal infinite decoy state case as well as the simulation of the original LM05, it can be said that a more refined method that based on the first approach should be considered as a proper estimation for a finite decoy implementation. On the whole, our practical approach does expectedly fall a little short with regards to the ideal infinite decoy case but really does improve the performance of the original even not as impressive as decoy state BB84 does. Hence we believe our result should provide a better perspective and effectively proposes for a more serious consideration of two-way protocols like LM05.