It is defined as a ratio between the secret key rate (at a given distance) and the amount of quantum resources (qubits) used in the QKD of concern. Furthermore, the work proposes a metric for evaluating the optimality of a QKD. The proposed relativistic models are compared to twin-field QKD protocols. Secret-key-rate comparison between distinct models is reported. Those values of rate are obtained without disturbing the security. The former scheme has lower secret key rate, but longer operating distances (the work could operate at distances of up to 320 km). However, the values for the secret key rate are relevant for distances of up to 150 km. The latter scheme has the highest secret key rate of all the relativistic QKD protocols. Both of the proposed schemes are characterized with high secret key rate. The other proposed scheme represents a setup of a classic relativistic QKD, but with slight modification. One of the proposed schemes is a system comprised of two sequentially connected interferometers, as the first (interferometer) controls the behavior of the second one. Both schemes rely on high-dimensional quantum systems (phase and polarization encodings are utilized for establishing key bits).

Here we report two point-to-point relativistic quantum key distribution schemes implemented with weak coherent pulses. However, the existing relativistic schemes have not demonstrated optimality in terms of efficiency and rate (including secret key rate). An optimal scheme in terms of security is the so-called relativistic quantum key distribution it ensures the security of the system by using both quantum phenomena and relativity. A great challenge in the field of quantum cryptography is the design and implementation of optimal quantum key distribution (QKD) scheme.

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