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Scientific Reports

On the (relation between) efficiency and secret key rate of QKD

Georgi Bebrov

Published Feb 13, 2024• 3 citations
Publisher

Abstract

The processes of evaluation and comparison play a vital role in the development of a scientific field. In the field of quantum cryptography (especially quantum key distribution, QKD), the so-called secret key rate is used for characterizing the performance of a protocol (scheme). However the current definition of this quantity is incomplete. It does not consider the classical communication process taking place in a QKD protocol. There exists a quantity that involves all the procedures (resources) in a communication process: it is the efficiency (total efficiency). This paper reports a definition of this parameter. Also the relation between the total efficiency and key rate is found. By means of this relation, the total secret key rate of a QKD protocol is expressed. An application of the total key rate is demonstrated: the original twin-field QKD (TF-QKD) is evaluated in terms of this rate. The paper also shows a comparison between the total key rate and the standard key rate of a TF-QKD.

DOI
10.1038/s41598-024-54246-y

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The processes of evaluation and comparison play a vital role in the development of a scientific field. In the field of quantum cryptography (especially quantum key distribution, QKD), the so-called secret key rate is used for characterizing the performance of a protocol (scheme). However the current definition of this quantity is incomplete. It does not consider the classical communication process taking place in a QKD protocol. There exists a quantity that involves all the procedures (resources) in a communication process: it is the efficiency (total efficiency). This paper reports a definition of this parameter. Also the relation between the total efficiency and key rate is found. By means of this relation, the total secret key rate of a QKD protocol is expressed. An application of the total key rate is demonstrated: the original twin-field QKD (TF-QKD) is evaluated in terms of this rate. The paper also shows a comparison between the total key rate and the standard key rate of a TF-QKD.
A great challenge in the field of quantum cryptography is the design and implementation of optimal quantum key distribution (QKD) scheme. 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. However, the existing relativistic schemes have not demonstrated optimality in terms of efficiency and rate (including secret key rate). Here we report two point-to-point relativistic quantum key distribution schemes implemented with weak coherent pulses. Both schemes rely on high-dimensional quantum systems (phase and polarization encodings are utilized for establishing key bits). 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. The other proposed scheme represents a setup of a classic relativistic QKD, but with slight modification. Both of the proposed schemes are characterized with high secret key rate. The latter scheme has the highest secret key rate of all the relativistic QKD protocols. However, the values for the secret key rate are relevant for distances of up to 150 km. The former scheme has lower secret key rate, but longer operating distances (the work could operate at distances of up to 320 km). Those values of rate are obtained without disturbing the security. Secret-key-rate comparison between distinct models is reported. The proposed relativistic models are compared to twin-field QKD protocols. Furthermore, the work proposes a metric for evaluating the optimality of a QKD. 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. It is shown that one of the proposed schemes in this article is the most optimal relativistic key distribution and more optimal than the original twin-field. It is also verified that the proposed schemes excels the original twin-field in terms of secret key rate, but for short distances.
Abstract Twin-field quantum key distribution (TF-QKD) and its variant protocols are highly attractive due to the advantage of overcoming the rate-loss limit for secret key rates of point-to-point QKD protocols. For variations of TF-QKD, the key point to ensure security is switching randomly between a code mode and a test mode. Among all TF-QKD protocols, their code modes are very different, e.g. modulating continuous phases, modulating only two opposite phases, and sending or not sending signal pulses. Here we show that, by discretizing the number of global phases in the code mode, we can give a unified view on the first two types of TF-QKD protocols, and demonstrate that increasing the number of discrete phases extends the achievable distance, and as a trade-off, lowers the secret key rate at short distances due to the phase post-selection.
Quantum key distribution (QKD) systems require optimal performance of both quantum and classical channels - utilizing as few as possible qubits and bits for establishing as many as possible key bits. Here we report a way to determine if a quantum key distribution model (or protocol) operates in an optimal behavior. This is accomplished by introducing a quantity, called optimality, which is the maximum over the total efficiency of a QKD under any circumstances (any values of QKD parameters). The optimality definition is given for the asymptotic operation of a QKD system - when infinitely many quantum systems are transferred/used in a quantum key distribution protocol or a quantum key distribution system is used infinitely many times. A way to attain the optimality is considered\textemdash implementation of a completely efficient QKD system (a combination of capacity-reaching quantum channel and a completely compressed classical channel) is presented. Optimal versions of BB84-QKD and twin-field QKD are introduced.
Quantum key distribution (QKD) generates information-theoretical secret keys between two parties based on the physical laws of quantum mechanics. Following the advancement in quantum communication networks, it becomes feasible and economical to combine QKD with classical optical communication through the same fiber using dense wavelength division multiplexing (DWDM) technology. This study proposes a detailed scheme of TF-QKD protocol with DWDM technology and analyzes its performance, considering the influence of quantum channel number and adjacent quantum crosstalk on the secret key rates. The simulation results show that the scheme further increases the secret key rate of TF-QKD and its variants. Therefore, this scheme provides a method for improving the secret key rate for practical quantum networks.
Abstract Quantum key distribution (QKD) offers a reliable solution to communication problems that require long-term data security. For its widespread use, however, the rate and reach of QKD systems must be improved. Twin-field (TF) QKD is a step forward toward this direction, with early demonstrations suggesting it can beat the current rate-versus-distance records. A recently introduced variant of TF-QKD is particularly suited for experimental implementation, and has been shown to offer a higher key rate than other variants in the asymptotic regime, where users exchange an infinite number of signals. Here, we extend the security of this protocol to the finite-key regime, showing that it can overcome the fundamental bounds on point-to-point QKD with ~1010 transmitted signals. In many practical regimes of interest, our analysis offers higher key rates than those of alternative variants. Moreover, some of the techniques we develop are applicable to the finite-key analysis of other QKD protocols.