Finite-key security analysis of quantum key distribution with imperfect light sources

In recent years, the gap between theory and practice in quantum key distribution (QKD) has been significantly narrowed, particularly for QKD systems with arbitrarily awed optical receivers. The status for QKD systems with imperfect light sources is however less satisfactory, in the sense that the resulting secure key rates are often overly-dependent on the quality of state preparation. This is especially the case when the channel loss is high. Very recently, to overcome this limitation, Tamaki et al proposed a QKD protocol based on the so-called rejected data analysis, and showed that its security|in the limit of infinitely long keys|is almost independent of any encoding flaw in the qubit space, being this protocol compatible with the decoy state method. Here, as a step towards practical QKD, we show that a similar conclusion is reached in the finite-key regime, even when the intensity of the light source is unstable. More concretely, we derive security bounds for a wide class of realistic light sources and show that the bounds are also efficient in the presence of high channel loss. Our results strongly suggest the feasibility of long distance provably-secure communication with imperfect light sources.Comment: 27 pages, 7 figure

Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection

We define rewinding operators that invert quantum measurements. Then, we define complexity classes ${\sf RwBQP}$, ${\sf CBQP}$, and ${\sf AdPostBQP}$ as sets of decision problems solvable by polynomial-size quantum circuits with a polynomial number of rewinding operators, cloning operators, and adaptive postselections, respectively. Our main result is that ${\sf BPP}^{\sf PP}\subseteq{\sf RwBQP}={\sf CBQP}={\sf AdPostBQP}\subseteq{\sf PSPACE}$. As a byproduct of this result, we show that any problem in ${\sf PostBQP}$ can be solved with only postselections of outputs whose probabilities are polynomially close to one. Under the strongly believed assumption that ${\sf BQP}\nsupseteq{\sf SZK}$, or the shortest independent vectors problem cannot be efficiently solved with quantum computers, we also show that a single rewinding operator is sufficient to achieve tasks that are intractable for quantum computation. In addition, we consider rewindable Clifford and instantaneous quantum polynomial time circuits.Comment: 29 pages, 3 figures, v2: Added Result 3 and improved Result

Security of quantum key distribution with iterative sifting

Several quantum key distribution (QKD) protocols employ iterative sifting. After each quantum transmission round, Alice and Bob disclose part of their setting information (including their basis choices) for the detected signals. The quantum phase of the protocol then ends when the numbers of detected signals per basis exceed certain pre-agreed threshold values. Recently, however, Pfister et al. [New J. Phys. 18 053001 (2016)] showed that iterative sifting makes QKD insecure, especially in the finite key regime, if the parameter estimation for privacy amplification uses the random sampling theory. This implies that a number of existing finite key security proofs could be flawed and cannot guarantee security. Here, we solve this serious problem by showing that the use of Azuma's inequality for parameter estimation makes QKD with iterative sifting secure again. This means that the existing protocols whose security proof employs this inequality remain secure even if they employ iterative sifting. Also, our results highlight a fundamental difference between the random sampling theorem and Azuma's inequality in proving security.Comment: 9 pages. We have found a flaw in the first version, which we have corrected in the revised versio

Quantum key distribution with correlated sources

Implementation security is a critical problem in quantum key distribution (QKD). With the advent of measurement-device-independent QKD, all security loopholes of the measurement unit have been closed. Securing the source, however, remains an elusive issue. Despite the tremendous progress made by developing security proofs that accommodate most typical source imperfections, such proofs usually disregard the effect of pulse correlations. That is, they disregard the fact that the state of an emitted signal can depend on the signals selected previously. Here, we close this gap by introducing a simple yet general method to prove the security of QKD with arbitrary pulse correlations. Our method is compatible with those security proofs that accommodate all the other source imperfections, thus paving the way towards achieving implementation security in QKD with arbitrary flawed devices. Moreover, we introduce a new security proof, which we call the reference technique, that provides high performance in the presence of source imperfections.Comment: This arXiv version contains some errata, please refer to the published paper for the correct versio

Optimization of treatment strategy

The purpose of this study was to predict the survival time of patients with malignant glioma after radiotherapy with high accuracy by considering additional clinical factors and optimize the prescription dose and treatment duration for individual patient by using a machine learning model. A total of 35 patients with malignant glioma were included in this study. The candidate features included 12 clinical features and 192 dose–volume histogram (DVH) features. The appropriate input features and parameters of the support vector machine (SVM) were selected using the genetic algorithm based on Akaike’s information criterion, i.e. clinical, DVH, and both clinical and DVH features. The prediction accuracy of the SVM models was evaluated through a leave-one-out cross-validation test with residual error, which was defined as the absolute difference between the actual and predicted survival times after radiotherapy. Moreover, the influences of various values of prescription dose and treatment duration on the predicted survival time were evaluated. The prediction accuracy was significantly improved with the combined use of clinical and DVH features compared with the separate use of both features (P < 0.01, Wilcoxon signed rank test). Mean ± standard deviation of the leave-one-out cross-validation using the combined clinical and DVH features, only clinical features and only DVH features were 104.7 ± 96.5, 144.2 ± 126.1 and 204.5 ± 186.0 days, respectively. The prediction accuracy could be improved with the combination of clinical and DVH features, and our results show the potential to optimize the treatment strategy for individual patients based on a machine learning model