Robust Interior Point Method for Quantum Key Distribution Rate Computation

Abstract

Security proof methods for quantum key distribution, QKD, that are based on the numerical key rate calculation problem, are powerful in principle. However, the practicality of the methods are limited by computational resources and the efficiency and accuracy of the underlying algorithms for convex optimization. We derive a stable reformulation of the convex nonlinear semidefinite programming, SDP, model for the key rate calculation problems. We use this to develop an efficient, accurate algorithm. The reformulation is based on novel forms of facial reduction, FR, for both the linear constraints and nonlinear relative entropy objective function. This allows for a Gauss-Newton type interior-point approach that avoids the need for perturbations to obtain strict feasibility, a technique currently used in the literature. The result is high accuracy solutions with theoretically proven lower bounds for the original QKD from the FR stable reformulation. This provides novel contributions for FR for general SDP.We report on empirical results that dramatically improve on speed and accuracy, as well as solving previously intractable problems.

Automated machine learning for secure key rate in discrete-modulated continuous-variable quantum key distribution

“…One is the quadrature phase-shift-keying (QPSK) heterodyne detection protocol [37], and the other is an improved QPSK homodyne detection protocol [43]. To collect a dataset for training neural networks, we generate secure key rates of both protocols by applying the same numerical method [37,40]. In the following, we briefly introduce how computing key rates can be transformed into a relevant convex objective function for numerical optimization.…”

“…This neural network model learns the mapping between input parameters and key rates from datasets generated by numerical methods, which supports the computation of secure key rates in real time [39]. However, the mapping complexity between input parameters and key rates depends on the solving complexity of discrete-modulated protocols' key rates through numerical approaches [40]. Selecting architectures and hyperparameters plays a critical role in the performance of a neural network.…”

Homodyne Detection Quadrature Phase Shift Keying Continuous-Variable Quantum Key Distribution with High Excess Noise Tolerance

“…Since the security deals with the discontinuity of modulation, the loophole of continuity is leaped over naturally. Brilliant numerical methods for security analysis are constantly emerging [38][39][40] and analysis methods follow up [41], even though the discrete modulation lacks U(n) symmetry. Finally, security against collective attacks in the asymptotic regime has been proved.…”

Neural network-based prediction of the secret-key rate of quantum key distribution

“…In CV-QKD, discrete modulation technology has attracted much attention [26,[34][35][36][37][38][39][40][41][42][43][44] because of its ability to reduce the requirements for modulation devices. However, due to the lack of symmetry, the security proof of discrete modulation CV-QKD also mainly relies on numerical methods [37][38][39][40][41][42]45].Unfortunately, calculating a secure key rate by numerical methods requires minimizing a convex function over all eavesdropping attacks related with the experimental data [46,47]. The efficiency of this optimization depends on the number of parameters of the QKD protocol.…”

“…For example, in discrete modulation CV-QKD, the number of parameters is generally 1000 − 3000 depending on the different choices of cutoff photon numbers [38]. This leads to the corresponding optimization possibly taking minutes or even hours [45]. Therefore, it is especially important to develop tools for calculating the key rate that are more efficient than numerical methods.In this work, we take the homodyne detection discrete-modulated CV-QKD [38] as an example to construct a neural network capable of predicting the secure key rate for the purpose of saving time and resource consumption.…”