Long Distance Quantum Key Distribution without Quantum Memory

A quantum cryptography scheme for lossy channel is proposed which does not employ quantum memory. The scheme also does not use quantum codes and is rather simple for practical implementation. The goal of quantum cryptography is to secretly distribute the key (a string of bits) between the two spatially separated legitimate users. The existing quantum cryptography schemes can be classified into three groups: 1) schemes based on non-orthogonal states (where arbitrary pair of non-orthogonal states can be used to carry information) [1]; 2) schemes based on EPR effect [2], and 3) schemes based on relativistic orthogonal states [3,4]. The secrecy of the last scheme [3,4] is provided by the combination of the quantum nature of the states used and the restriction on the maximum possible speed of information transfer imposed by special relativity. Losses in the communication channel present a substantial obstacle in the way of practical applications of quantum cryptography. For fiber optics the typical attenuation is ∼ 0.2 db/km thus limiting the quantum cryptography systems to the lengths of a few tens kilometers. Because of the exponential growth of the number of attempts required to transmit a single bit of the secret key with the lossy channel length (n ∼ e L ch /L dec), usage of repeaters seems to be the only practical way of building a quantum cryptosystem over the distances substantially exceeding the attenuation length. Proposed in Ref. [5] was a quantum cryptosystem employing quantum memory cells at the intermediate sites to produce an EPR-pair (where the states localized at the channel ends are entangled) which is then used to generate the secret bit in a key according to the scheme proposed in Ref. [2]. In the scheme of Ref. [5] the repeaters with quantum memory are used to extend the entanglement over the entire length of the quantum communication channel. Below I outline a repeaters-based quantum cryptosystem avoiding the use of quantum memory. A fundamental difference of the proposed cryptosystem from that of Ref. [5] is that no entanglement swapping is required at the intermediate sites; instead, only classical information on the secret bit is processed within each site. Therefore, the proposed cryptosystem does not need quantum memory. The key is generated at each segment of the communication channel independently using a pair of orthogonal states as described in Ref. [3] or Ref. [4]. The secret keys thus obtained for different segments are then …