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In recent research, there has been a significant focus on establishing robust quantum cryptography using the continuous-variable quantum key distribution (CV-QKD) protocol based on Gaussian modulation of coherent states (GMCS). Unlike more stable fiber channels, one challenge faced in free-space quantum channels is the complex transmittance characterized by varying atmospheric turbulence. This complexity poses difficulties in achieving high transmission rates and long-distance communication. In this article, we thoroughly evaluate the performance of the CV-QKD/GMCS system under the effect of individual attacks, considering homodyne detection with both direct and reverse reconciliation techniques. To address the issue of limited detector efficiency, we incorporate the phase-sensitive amplifier (PSA) as a compensating measure. The results show that the CV-QKD/GMCS system with PSA achieves a longer secure distance and a higher key rate compared to the system without PSA, considering both direct and reverse reconciliation algorithms. With an amplifier gain of 10, the reverse reconciliation algorithm achieves a secure distance of 5 km with a secret key rate of 10-1 bits/pulse. On the other hand, direct reconciliation reaches a secure distance of 2.82 km.

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BACKGROUND: Body mass index (BMI) serves as a global metric for assessing obesity and overall health status. However, the impact of BMI, treated as a continuous variable, on the risk of perioperative stroke remains poorly understood. This retrospective cohort study aimed to elucidate the association between BMI and the risk of perioperative ischemic stroke in patients undergoing non-cardiovascular surgery. METHODS: A cohort of 223,415 patients undergoing noncardiac surgery at the First Medical Center of Chinese PLA General Hospital between January 1, 2008 and August 31, 2019 was screened. Preoperative high BMI, defined as BMI >22.64 kg/m2, was the primary exposure, and the outcome of interest was the new diagnosis of perioperative ischemic stroke within 30 days post-surgery. Robust controls for patient and intraoperative factors were implemented to minimize residual confounding. Logistic regression and propensity score matching were employed, and patients were stratified into subgroups for further investigation. RESULTS: The overall incidence of perioperative ischemic stroke was 0.23% (n = 525) in the cohort. After adjusting for patient-related variables (OR 1.283; 95% CI, 1.04-1.594; p < 0.05), surgery-related variables (OR 1.484; 95% CI, 1.2-1.849; p < 0.001), and all confounding variables (OR 1.279; 95% CI, 1.025-1.607; p < 0.05), patients with BMI >22.64 kg/m2 exhibited a significantly increased risk of perioperative ischemic stroke. This association persisted in the propensity score matched cohort (OR 1.577; 95% CI, 1.203-2.073; p < 0.01). Subgroup analyses indicated that preoperative BMI >22.64 kg/m2 correlated with an elevated risk of perioperative ischemic stroke in female patients, those with coronary heart disease, peripheral vascular diseases, and individuals undergoing neurosurgery. CONCLUSION: We first identified BMI >22.64 kg/m2 as a substantial and independent risk factor for perioperative ischemic stroke in Chinese noncardiac surgery patients. Normal BMI may not suffice as a universal preventive standard. Instead, a more stringent perioperative weight management approach is recommended, particularly for specific subgroups such as female patients, those with coronary heart disease and peripheral vascular disease, and individuals scheduled for neurosurgery.

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The wavelength attack utilizes the dependence of beam splitters (BSs) on wavelength to cause legitimate users Alice and Bob to underestimate their excess noise so that Eve can steal more secret keys without being detected. Recently, the wavelength attack on Gaussian-modulated continuous-variable quantum key distribution (CV-QKD) has been researched in both fiber and atmospheric channels. However, the wavelength attack may also pose a threat to the case of ocean turbulent channels, which are vital for the secure communication of both ocean sensor networks and submarines. In this work, we propose two wavelength attack schemes on underwater discrete modulated (DM) CV-QKD protocol, which is effective for the case with and without local oscillator (LO) intensity monitor, respectively. In terms of the transmittance properties of the fused biconical taper (FBT) BS, two sets of wavelengths are determined for Eve's pulse manipulation, which are all located in the so-called blue-green band. The derived successful criterion shows that both attack schemes can control the estimated excess noise of Alice and Bob close to zero by selecting the corresponding condition parameters based on channel transmittance. Additionally, our numerical analysis shows that Eve can steal more bits when the wavelength attack controls the value of the estimated excess noise closer to zero.

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An entanglement-based continuous variable (CV) QKD scheme is proposed, performing information reconciliation over an entanglement-assisted link. The same entanglement generation source is used in both raw key transmission and information reconciliation. The entanglement generation source employs only low-cost devices operated in the C-band. The proposed CV-QKD scheme with information reconciliation over an entanglement-assisted link significantly outperforms the corresponding CV-QKD scheme with information reconciliation over an authenticated public channel. It also outperforms the CV-QKD scheme in which a classical free-space optical communication link is used to perform information reconciliation. An experimental demonstration over the free-space optical testbed established at the University of Arizona campus indicates that the proposed CV-QKD can operate in strong turbulence regimes. To improve the secret key rate performance further, adaptive optics is used.

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Building an underwater quantum network is necessary for various applications such as ocean exploration, environmental monitoring, and national defense. Motivated by characteristics of the oceanic turbulence channel, we suggest a machine learning approach to predicting the channel characteristics of continuous variable (CV) quantum key distribution (QKD) in challenging seawater environments. We consider the passive continuous variable (CV) measurement-device-independent (MDI) QKD in oceanic scenarios, since the passive-state preparation scheme offers simpler linear elements for preparation, resulting in reduced interaction with the practical environment. To provide a practical reference for underwater quantum communications, we suggest a prediction of transmittance for the ocean quantum links with a given neural network as an example of machine learning algorithms. The results have a good consistency with the real data within the allowable error range; this makes the passive CVQKD more promising for commercialization and implementation.

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BACKGROUND: Medical image registration plays an important role in several applications. Existing approaches using unsupervised learning encounter issues due to the data imbalance problem, as their target is usually a continuous variable. OBJECTIVE: In this study, we introduce a novel approach known as Unsupervised Imbalanced Registration, to address the challenge of data imbalance and prevent overconfidence while increasing the accuracy and stability of 4D image registration. METHODS: Our approach involves performing unsupervised image mixtures to smooth the input space, followed by unsupervised image registration to learn the continual target. We evaluated our method on 4D-Lung using two widely used unsupervised methods, namely VoxelMorph and ViT-V-Net. RESULTS: Our findings demonstrate that our proposed method significantly enhances the mean accuracy of registration by 3%-10% on a small dataset while also reducing the accuracy variance by 10%. CONCLUSION: Unsupervised Imbalanced Registration is a promising approach that is compatible with current unsupervised image registration methods applied to 4D images.

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OBJECTIVES: Randomized controlled trials (RCTs) with repeatedly measured continuous variables as primary outcomes are common. Although statistical methodologies for calculating sample sizes in such trials have been extensively investigated, their practical application remains unclear. This study aims to provide an overview of sample size calculation methods for different research questions (e.g., key time point treatment effect, treatment effect change over time) and evaluate the adequacy of current practices in trial design. STUDY DESIGN AND SETTING: We conducted a comprehensive search of PubMed to identify RCTs published in core journals in 2019 that utilized repeatedly measured continuous variables as their primary outcomes. Data were extracted using a predefined questionnaire including general study characteristics, primary outcomes, detailed sample size calculation methods, and methods for analyzing the primary outcome. We re-estimated the sample size for trials that provided all relevant parameters. RESULTS: A total of 168 RCTs were included, with a median of four repeated measurements (interquartile range 3-6) per outcome. In 48 (28.6%) trials, the primary outcome used for sample size calculation differed from the one used in defining the primary outcomes. There were 90 (53.6%) trials exhibited inconsistencies between the hypotheses specified for sample size calculation and those specified for primary analysis. The statistical methods used for sample size calculation in 158 (94.0%) trials did not align with those used for primary analysis. Additionally, only 6 (3.6%) trials accounted for the number of repeated measurements, and 7 (4.2%) trials considered the correlation among these measurements when calculating the sample size. Furthermore, of the 128 (76.2%) trials that considered loss to follow-up, 33 (25.8%) used an incorrect formula (i.e., N∗(1+lose rate) for sample size adjustment. In 53 (49.5%) out of 107 trials, the re-estimated sample size was larger than the reported sample size. CONCLUSION: The practice of sample size calculation for RCTs with repeatedly measured continuous variables as primary outcomes displayed significant deficiencies, with a notable proportion of trials failed to report essential parameters about repeated measurement required for sample size calculation. Our findings highlight the urgent need to use optimal sample size methods that align with the research hypothesis, primary analysis method, and the form of the primary outcome.

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The Jordan-Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator creation and annihilation operators acting in the Hilbert space of quantum oscillator states. Then, to describe quantum states in the probability representation of quantum oscillator states, we express their density operators in terms of conditional probability distributions (symplectic tomograms) or Husimi-like probability distributions. We illustrate this general scheme by examples of qubit states (spin-1/2 su(2)-group states) and even and odd Schrödinger cat states related to the other representation of su(2)-algebra (spin-j representation). The two-mode coherent-state superpositions associated with cyclic groups are studied, using the Jordan-Schwinger map. This map allows us to visualize and compare different properties of the mentioned states. For this, the su(2) coherent states for different angular momenta j are used to define a Husimi-like Q representation. Some properties of these states are explicitly presented for the cyclic groups C2 and C3. Also, their use in quantum information and computing is mentioned.

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Continuous-variable quantum key distribution (CV-QKD) is a promising protocol that can be easily integrated with classical optical communication systems. However, in the case of quantum-classical co-transmissions, such as dense wavelength division multiplexing with classical channels and time division multiplexing with large-power classical signal, a quantum signal is more susceptible to crosstalk caused by a classical signal, leading to signal distortion and key distribution performance reduction. To address this issue, we propose a noise-suppression scheme based on carrier frequency switching (CFS) that can effectively mitigate the influence of large-power random noise on the weak coherent state. In this noise-suppression scheme, a minimum-value window of the channel's noise power spectrum is searched for and the transmission signal frequency spectrum shifts to the corresponding frequency to avoid large-power channel noise. A digital filter is also utilized to filter out most of the channel noise. Simulation results show that compared to the traditional fixed carrier frequency scheme, the proposed noise-suppression scheme can reduce the excess noise to 1.8%, and the secret key rate can be increased by 1.43 to 2.86 times at different distances. This noise-suppression scheme is expected to be applied in scenarios like quantum-classical co-transmission and multi-QKD co-transmission to provide noise-suppression solutions.

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We consider the concept of velocity fields, taken from Bohmian mechanics, to investigate the dynamical effects of entanglement in bipartite realizations of Young's two-slit experiment. In particular, by comparing the behavior exhibited by factorizable two-slit states (cat-type state analogs in the position representation) with the dynamics exhibited by a continuous-variable Bell-type maximally entangled state, we find that, while the velocity fields associated with each particle in the separable scenario are well-defined and act separately on each subspace, in the entangled case there is a strong deformation in the total space that prevents this behavior. Consequently, the trajectories for each subsystem are not constrained any longer to remain confined within the corresponding subspace; rather, they exhibit seemingly wandering behavior across the total space. In this way, within the subspace associated with each particle (that is, when we trace over the other subsystem), not only interference features are washed out, but also the so-called Bohmian non-crossing rule (i.e., particle trajectories are allowed to get across the same point at the same time).

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Quantum Key Distribution (QKD) is a cutting-edge communication method that enables secure communication between two parties. Continuous-variable QKD (CV-QKD) is a promising approach to QKD that has several advantages over traditional discrete-variable systems. Despite its potential, CV-QKD systems are highly sensitive to optical and electronic component impairments, which can significantly reduce the secret key rate. In this research, we address this challenge by modeling a CV-QKD system to simulate the impact of individual impairments on the secret key rate. The results show that laser frequency drifts and small imperfections in electro-optical devices such as the beam splitter and the balanced detector have a negative impact on the secret key rate. This provides valuable insights into strategies for optimizing the performance of CV-QKD systems and overcome limitations caused by component impairments. By offering a method to analyze them, the study enables the establishment of quality standards for the components of CV-QKD systems, driving the development of advanced technologies for secure communication in the future.

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Continuous-variable quantum key distribution (CVQKD) plays an important role in quantum communications, because of its compatible setup for optical implementation with low cost. For this paper, we considered a neural network approach to predicting the secret key rate of CVQKD with discrete modulation (DM) through an underwater channel. A long-short-term-memory-(LSTM)-based neural network (NN) model was employed, in order to demonstrate performance improvement when taking into account the secret key rate. The numerical simulations showed that the lower bound of the secret key rate could be achieved for a finite-size analysis, where the LSTM-based neural network (NN) was much better than that of the backward-propagation-(BP)-based neural network (NN). This approach helped to realize the fast derivation of the secret key rate of CVQKD through an underwater channel, indicating that it can be used for improving performance in practical quantum communications.

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BACKGROUND: The multivariable fractional polynomial (MFP) approach combines variable selection using backward elimination with a function selection procedure (FSP) for fractional polynomial (FP) functions. It is a relatively simple approach which can be easily understood without advanced training in statistical modeling. For continuous variables, a closed test procedure is used to decide between no effect, linear, FP1, or FP2 functions. Influential points (IPs) and small sample sizes can both have a strong impact on a selected function and MFP model. METHODS: We used simulated data with six continuous and four categorical predictors to illustrate approaches which can help to identify IPs with an influence on function selection and the MFP model. Approaches use leave-one or two-out and two related techniques for a multivariable assessment. In eight subsamples, we also investigated the effects of sample size and model replicability, the latter by using three non-overlapping subsamples with the same sample size. For better illustration, a structured profile was used to provide an overview of all analyses conducted. RESULTS: The results showed that one or more IPs can drive the functions and models selected. In addition, with a small sample size, MFP was not able to detect some non-linear functions and the selected model differed substantially from the true underlying model. However, when the sample size was relatively large and regression diagnostics were carefully conducted, MFP selected functions or models that were similar to the underlying true model. CONCLUSIONS: For smaller sample size, IPs and low power are important reasons that the MFP approach may not be able to identify underlying functional relationships for continuous variables and selected models might differ substantially from the true model. However, for larger sample sizes, a carefully conducted MFP analysis is often a suitable way to select a multivariable regression model which includes continuous variables. In such a case, MFP can be the preferred approach to derive a multivariable descriptive model.

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We employ an exact solution of the thermal bath Lindblad master equation with the Liouvillian superoperator that takes into account both dynamic and environment-induced intermode couplings to study the speed of evolution and quantum speed limit (QSL) times of a open multi-mode bosonic system. The time-dependent QSL times are defined from quantum speed limits, giving upper bounds on the rate of change of two different measures of distinguishability: the fidelity of evolution and the Hilbert-Schmidt distance. For Gaussian states, we derive explicit expressions for the evolution speed and the QSL times. General analytical results are applied to the special case of a two-mode system where the intermode couplings can be characterized by two intermode coupling vectors: the frequency vector and the relaxation rate vector. For the system initially prepared in a two-mode squeezed state, dynamical regimes are generally determined by the intermode coupling vectors, the squeezing parameter and temperature. When the vectors are parallel, different regimes may be associated with the disentanglement time, which is found to be an increasing (a decreasing) function of the length of the relaxation vector when the squeezing parameter is below (above) its temperature-dependent critical value. Alternatively, we study dynamical regimes related to the long-time asymptotic behavior of the QSL times, which is characterized by linear time dependence with the proportionality coefficients defined as the long-time asymptotic ratios. These coefficients are evaluated as a function of the squeezing parameter at varying temperatures and relaxation vector lengths. We also discuss how the magnitude and orientation of the intermode coupling vectors influence the maximum speed of evolution and dynamics of the entropy and the mutual information.

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The estimation of phase noise of continuous-variable quantum key distribution protocol with a local local oscillator (LLO CVQKD), as a major process in quantifying the secret key rate, is closely relevant to the intensity of the phase reference. However, the transmission of the phase reference through the insecure quantum channel is prone to be exploited by the eavesdropper (Eve) to mount attacks. Here, we introduce a polarization attack scheme against the phase reference. Presently, in a practical LLO CVQKD system, only part of the phase reference pulses are measured to compensate for the polarization drift of the quantum signal pulses in a compensation cycle due to the limited polarization measurement rate, while the other part of the phase reference pulses are not measured. We show that Eve can control the phase noise by manipulating the polarization direction of the unmeasured phase reference to hide her attack on the quantum signal. Simulations show that Eve can obtain partial or total key rates information shared between Alice and Bob as the transmission distance increases. Improving the polarization measurement rate to 100% or monitoring the phase reference intensity in real-time is of great importance to protect the LLO CVQKD from polarization attack.

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A saturation attack can be employed for compromising the practical security of continuous-variable quantum key distribution (CVQKD). In this paper, we suggest a countermeasure approach to resisting this attack by embedding an adjustable optical filter (AOF) in the CVQKD system. Numerical simulations illustrate the effects of the AOF-enabled countermeasure on the performance in terms of the secret key rate and transmission distance. The legal participants can trace back the information that has been eavesdropped by an attacker from the imperfect receiver, which indicates that this approach can be used for defeating a saturation attack in practical quantum communications.

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Continuous-variable measure-device-independent quantum key distribution (CV-MDI QKD) is proposed to remove all imperfections originating from detection. However, there are still some inevitable imperfections in a practical CV-MDI QKD system. For example, there is a fluctuating channel transmittance in the complex communication environments. Here we investigate the security of the system under the effects of the fluctuating channel transmittance, where the transmittance is regarded as a fixed value related to communication distance in theory. We first discuss the parameter estimation in fluctuating channel transmittance based on these establishing of channel models, which has an obvious deviation compared with the estimated parameters in the ideal case. Then, we show the evaluated results when the channel transmittance respectively obeys the two-point distribution and the uniform distribution. In particular, the two distributions can be easily realized under the manipulation of eavesdroppers. Finally, we analyze the secret key rate of the system when the channel transmittance obeys the above distributions. The simulation analysis indicates that a slight fluctuation of the channel transmittance may seriously reduce the performance of the system, especially in the extreme asymmetric case. Furthermore, the communication between Alice, Bob and Charlie may be immediately interrupted. Therefore, eavesdroppers can manipulate the channel transmittance to complete a denial-of-service attack in a practical CV-MDI QKD system. To resist this attack, the Gaussian post-selection method can be exploited to calibrate the parameter estimation to reduce the deterioration of performance of the system.

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Long block length rate-compatible low-density parity-compatible (LDPC) codes are designed to solve the problems of great variation of quantum channel noise and extremely low signal-to-noise ratio in continuous-variable quantum key distribution (CV-QKD). The existing rate-compatible methods for CV-QKD inevitably cost abundant hardware resources and waste secret key resources. In this paper, we propose a design rule of rate-compatible LDPC codes that can cover all potential SNRs with single check matrix. Based on this long block length LDPC code, we achieve high efficiency continuous-variable quantum key distribution information reconciliation with a reconciliation efficiency of 91.80% and we have higher hardware processing efficiency and lower frame error rate than other schemes. Our proposed LDPC code can obtain a high practical secret key rate and a long transmission distance in an extremely unstable channel.

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We propose a multidimensional reconciliation encoding algorithm based on a field-programmable gate array (FPGA) with variable data throughput that enables quantum key distribution (QKD) systems to be adapted to different throughput requirements. Using the circulatory structure, data flow in the most complex pipeline operation in the same time interval, which enables the structural multiplexing of the algorithm. We handle the calculation and storage of eight-dimensional matrices cleverly to conserve resources and increase data processing speed. In order to obtain the syndrome more efficiently, we designed a simplified algorithm according to the characteristics of the FPGA and parity-check matrix, which omits the unnecessary operation of matrix multiplication. The simplified algorithm could adapt to different rates. We validated the feasibility and high speed of the algorithm by implementing the multidimensional reconciliation encoding algorithm on a Xilinx Virtex-7 FPGA. Our simulation results show that the maximum throughput could reach 4.88 M symbols/s.

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We perform security analysis of a passive continuous-variable quantum key distribution (CV-QKD) protocol by considering the finite-size effect. In the passive CV-QKD scheme, Alice utilizes thermal sources to passively make preparation of quantum state without Gaussian modulations. With this technique, the quantum states can be prepared precisely to match the high transmission rate. Here, both asymptotic regime and finite-size regime are considered to make a comparison. In the finite-size scenario, we illustrate the passive CV-QKD protocol against collective attacks. Simulation results show that the performance of passive CV-QKD protocol in the finite-size case is more pessimistic than that achieved in the asymptotic case, which indicates that the finite-size effect has a great influence on the performance of the single-mode passive CV-QKD protocol. However, we can still obtain a reasonable performance in the finite-size regime by enhancing the average photon number of the thermal state.