Erroneous signal detection and secure distance improvement in two way Quantum Key Distribution protocol with decoy state

The erroneous signal detection characterizes the quality of alignment and stability of a Quantum Key Distribution (QKD) system. Its effect against the improvement to the maximum secure distance achievable with weak+vacuum decoy state and a two way Quantum Key Distribution protocol, namely the LM05 protocol is investigated. The result from our numerical simulation suggested that the secure distance improvement for the two key rate formulas are stable only when erroneous signal detection is at below 5%. Interestingly, at beyond 5 %, the two secure key rate formulas exhibit opposite result with one tends to increase while the other tends to decrease.