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arXiv:1710.05511 · Quantum

Reliable numerical key rates for quantum key distribution

Adam Winick, Norbert Lütkenhaus, Patrick J. Coles

Published Jul 26, 2018• 138 citations
arXivHTMLPDF

Abstract

In this work, we present a reliable, efficient, and tight numerical method for calculating key rates for finite-dimensional quantum key distribution (QKD) protocols. We illustrate our approach by finding higher key rates than those previously reported in the literature for several interesting scenarios (e.g., the Trojan-horse attack and the phase-coherent BB84 protocol). Our method will ultimately improve our ability to automate key rate calculations and, hence, to develop a user-friendly software package that could be used widely by QKD researchers.

DOI
10.22331/q-2018-07-26-77

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In this work, we present a reliable, efficient, and tight numerical method for calculating key rates for finite-dimensional quantum key distribution (QKD) protocols. We illustrate our approach by finding higher key rates than those previously reported in the literature for several interesting scenarios (e.g., the Trojan-horse attack and the phase-coherent BB84 protocol). Our method will ultimately improve our ability to automate key rate calculations and, hence, to develop a user-friendly software package that could be used widely by QKD researchers.
This thesis applies numerical methods to analyze the security of quantum key distribution (QKD) protocols. The main theoretical problem in QKD security proofs is to calculate the secret key generation rate. Under certain assumptions, this problem has been formulated as a convex optimization problem and numerical methods have been proposed to produce reliable lower bounds for discrete-variable QKD protocols. We investigate the applicability of these numerical approaches and apply the numerical methods to study a variety of protocols, including measurement-device-independent (MDI) protocols, variations of the BB84 protocol with a passive countermeasure against Trojan horse attacks, and the phase-encoding BB84 protocol using attenuated laser sources without continuous phase randomization.
Quantum key distribution (QKD) allows for communication with security guaranteed by quantum theory. The main theoretical problem in QKD is to calculate the secret key rate for a given protocol. Analytical formulas are known for protocols with a high degree of symmetry, since symmetry simplifies the analysis. However, experimental imperfections break symmetries, hence the effect of imperfections on key rates is difficult to estimate. Furthermore, it is an interesting question whether (intentionally) asymmetric protocols could outperform symmetric ones. In this work, we develop a robust numerical approach for calculating the key rate for arbitrary discrete-variable QKD protocols. This will allow researchers to study “unstructured” protocols, i.e., those that lack symmetry. Our approach relies on transforming the key rate calculation to the dual optimization problem, which dramatically reduces the number of parameters and hence the calculation time. We illustrate our method, first, by reproducing known literature results for some famous QKD protocols and, second, by investigating some unstructured protocols for which the key rate was previously unknown. Ultimately our vision is to develop user-friendly software that will allow researchers to assess the performance of any QKD protocol simply by running a MATLAB script on their laptop computer. We have taken a step towards that goal by making the key rate calculation more time-efficient. Further details about our work can be found in the following preprint: http://arxiv.org/abs/1510.01294.
Quantum key distribution (QKD) allows for communication with security guaranteed by quantum theory. The main theoretical problem in QKD is to calculate the secret key rate for a given protocol. Analytical formulas are known for protocols with symmetries, since symmetry simplifies the analysis. However, experimental imperfections break symmetries, hence the effect of imperfections on key rates is difficult to estimate. Furthermore, it is an interesting question whether (intentionally) asymmetric protocols could outperform symmetric ones. Here we develop a robust numerical approach for calculating the key rate for arbitrary discrete-variable QKD protocols. Ultimately this will allow researchers to study 'unstructured' protocols, that is, those that lack symmetry. Our approach relies on transforming the key rate calculation to the dual optimization problem, which markedly reduces the number of parameters and hence the calculation time. We illustrate our method by investigating some unstructured protocols for which the key rate was previously unknown.
Quantum key distribution (QKD) can be proved to be secure by laws of quantum mechanics. In this thesis, we review security proof methods in Renner's framework and discuss numerical methods to calculate asymptotic and finite key rates. These methods are highly versatile and applicable to general device-dependent QKD protocols. We also discuss analytical tools that extend the applicability of these numerical methods. We then present the asymptotic security proof against collective attacks for a variant of the twin-field QKD protocol, which can overcome the repeaterless secret-key capacity bound. Our variant reduces the sifting cost and uses non-phase-randomized coherent states as both signals and test states. We confirm the loss scaling of this protocol. Another important family of protocols that we investigate here are discrete-modulated continuous-variable QKD protocols. They are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks. Our security proof method can provide tight asymptotic key rates. We demonstrate that the postselection of data in combination with reverse reconciliation can improve the key rates. We analyze both untrusted and trusted detector noise scenarios. Our results in the trusted detector noise scenario show that we can thus cut out most of the effect of detector noise and obtain asymptotic key rates similar to those had we access to ideal detectors. Finally, we present several simple examples to illustrate our newly developed method for the numerical finite-key analysis against the most general attacks via the entropy accumulation theorem.
Abstract Quantum key distribution (QKD) is a secure communication method that relies on the inherent randomness of quantum mechanics to ensure information-theoretic security. The first and most widely used QKD protocol is BB84, and the proof of BB84's security is vital. The Discrete Phase Randomized BB84 protocol is a variant of the decoy BB84 protocol. It has been proven to be promising in the development of high-speed QKD systems. However, it still lacks an analysis with a finite number of pulses. This paper presents a comprehensive security analysis of the discrete phase BB84 protocol, using two different methods under different conditions. The analysis involves simulations and optimizations to determine the optimal parameter settings. It is confirmed that for typical scenarios, if the number of discrete phases exceeds 30, one can calculate the key rate by assuming that a continuous phase randomization process was in operation. On the other hand, for a relatively smaller number of discrete values, we have developed a numerical method to calculate the key rate. We have confirmed that its performance is reduced but still acceptable with a finite number of pulses.
Quantum key distribution (QKD) enables secure information exchange with untrusted quantum links between remote communication parties. A central task in the studies of QKD protocols is security analysis, which aims at deriving the length of the final key such that it is secure regardless of the eavesdropper's computational power. In literature, the security analysis has been done both analytically and numerically. Compared to analytical methods which tend to require techniques specific to each QKD protocol, numerical ones are more general since they can be directly applied to many QKD protocols with little adaptation. However, current numerical methods are carried out based on some assumptions such as working in the asymptotic limit and collective attacks from eavesdroppers. In this work, we remove these assumptions and develop a numerical finite-size security analysis against general attacks for a large class of QKD protocols. We also give an example of applying the method to the recent phase-matching QKD protocol with a simplified protocol design. Our result shows that the finite-size key rate can surpass the linear key-rate bound with a practical QKD system operated for only several hours.