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Quantum cryptography was proposed as a counter to the capacity of quantum computers to break classical cryptosystems. A broad subclass of quantum cryptography, called quantum key distribution (QKD), relies on quantum mechanical process for secure distribution of the keys. Quantum channels are inherently noisy, and therefore these protocols will be susceptible to noise as well. In this paper, we study the performance of two QKD protocols — BB84 and E91 under amplitude damping error. We show that while E91 protocol loses its security immediately due to loss of entanglement, the performance of BB84 protocol reduces to random guessing with increasing time. Next, we consider the action of an Eve on the BB84 protocol under amplitude damping noise, who is restricted to guessing the outcome of the protocol only. Under this restriction, we show that Eve can still do better than random guessing when equipped with the characteristics of the noisy channel. Finally, we propose a modification of the BB84 protocol which retains the security of the original protocol, but ensures that Eve cannot get any advantage in guessing the outcome, even with complete channel information.

Quantum key distribution (QKD) is a proven secured way to transmit shared secret keys using quantum particles. Any adversarial attempt to intercept and eavesdrop secret key results in generating errors alerting the legitimate users. Since QKD is constrained by quantum mechanics principles, the practical transmission of the key at a greater distance is an issue. In this paper, we discover and analyze the key factors associated with transmission media, hardware components and protocol implementation of the QKD system that causes hindrance in distance range. Practical implementation of BB84 and KMB09 protocols is discussed to determine the achievable distance given current technology. We find that by using ultra low loss fiber, short-pulse laser and superconducting nanowire single photon detector the maximum achievable distance for both of the quantum protocols is 250km.