Phase synchronization from noisy univariate signals

We present methods for detecting phase synchronization of two unidirectionally coupled, self-sustained noisy oscillators from a signal of the driven oscillator alone. One method detects soft phase locking; another hard phase locking. Both are applied to the problem of detecting phase synchronization in von Kármán vortex flow meters.     

Morphogen gradient from a noisy source

We investigate the effect of time-dependent noise on the shape of a morphogen gradient in a developing embryo. Perturbation theory is used to calculate the deviations from deterministic behavior in a simple reaction-diffusion model of robust gradient formation, and the results are confirmed by numerical simulation. It is shown that such deviations can disrupt robustness for sufficiently high noise levels, and the implications of these findings for more complex models of gradient-shaping pathways are discussed.     

Quantum Cryptography

Quantum cryptography makes use of the quantum-mechanical behavior of nature for the design and analysis of cryptographic schemes. Optimally (but not always), quantum cryptography allows for the design of cryptographic schemes whose security is guaranteed solely by the laws of nature. This is in sharp contrast to standard cryptographic schemes, which can be broken in principle, i.e., when given sufficient computing power. From a theory point of view, quantum cryptography offers a beautiful interplay between the mathematics of adversarial behavior and quantum information theory. In this review article, we discuss the traditional application of quantum cryptography, quantum key distribution (QKD), from a modern perspective, and we discuss some recent developments in the context of quantum two-party cooperation (2PC). QKD allows two distant parties to communicate in a provably-secure way in the presence of an outside eavesdropper, whereas 2PC is concerned with protecting information against possibly malicious insiders. We show the basic idea of constructing quantum cryptographic schemes, but we also show some connections to quantum information theory as needed for the rigorous security analyses, and we discuss some of the relevant quantum-information-theoretic results.     

Invisible Visual Cryptography

We propose to realize visual cryptography in an indirect way with the help of diffractive optics, the pure-amplitude keys being substituted with the phase-only keys that are invisible for common-used intensity detectors, leading to the significantly enhanced security and improved usability for practice. Three typical realizations are provided by using static or dynamic diffractive optical elements, and the new concept of invisible visual cryptography(IVC)may be established. This concept is demonstrated by a compact opto-electronic system with only one spatial light modulator within time-delayed exposure, maintaining the fast speed of decryption and no requirement to the calculation of decryption in conventional visual cryptography. Further, IVC shows the immunity to noises and good information capacity, which is partly inherited from diffractive optics. IVC might suggest a new strategy for visual cryptography with the respective of diverse realizations, such as opto-electronic or even bio-chemical or other methods.     

Optimal squeezing and entanglement from noisy Gaussian operations

We investigate the creation of squeezing via operations subject to noise and losses and ask for the optimal use of such devices when supplemented by noiseless passive operations. Both single and repeated uses of the device are optimized analytically and it is proven that in the latter case the squeezing converges exponentially fast to its asymptotic optimum, which we determine explicitly. For the case of multiple iterations we show that the optimum can be achieved with fixed intermediate passive operations. Finally, we relate the results to the generation of entanglement and derive the maximal two-mode entanglement achievable within the considered scenario.     

Maximum-entropy reconstruction of two-body potentials from noisy scattering amplitudes

A maximum-entropy method of data analysis previously applied in astrophysics is adapted to the problem of obtaining the shape of a central potential from noisy scattering-amplitude data. The method is applied to a simplified nucleon-nucleon scattering problem in the case where the interaction is purely repulsive. The entropy of the potential distribution is maximized subject to the constraint that the scattering-amplitude data, which is related to the potential distribution through a Born integral plus gaussian noise, has a χ² per degree of freedom of 1. Good results, limited only by the quality of the data and the maximum value of the momentum transfer used, are obtained for synthetic data generated from exponential and gaussian potentials.     

Average trajectories and fluctuations from noisy,nonlinear maps

The average trajectories and fluctuations around them resulting from an ensemble of noisy, nonlinear maps are analyzed. The bifurcation diagram for the average value obtained from the computer simulation of noisy maps ensemble is discussed first. Then a deterministic average equation of motion describing in an approximate way the time evolution of the average value and of the variance is analyzed numerically. This equation predicts the existence of the bifurcation gap and of the exceptional attractors for special initial points. The scaling properties of the average value and of the variance are obtained with the help of this equation.On leave from Institute for Theoretical Physics, Warsaw University, 00-681 Warsaw, Hoza 69, Poland.     

A Three-Stage Quantum Cryptography Protocol

We present a three-stage quantum cryptographic protocol based on public key cryptography in which each party uses its own secret key. Unlike the BB84 protocol, where the qubits are transmitted in only one direction and classical information exchanged thereafter, the communication in the proposed protocol remains quantum in each stage. A related system of key distribution is also described.     

Quantum Cryptography in Spin Networks

In this paper we propose a new scheme of long-distance quantum cryptography based on spin networks with qubits stored in electron spins of quantum dots. By＂ conditional Faraday- rotation, single photon polarization measurement, and quantum state transfer, maximal-entangled Bell states for quantum cryptography between two long-distance parties are created. Meanwhile, efficient quantum state transfer over arbitrary＂ distances is obtained in a spin chain by＂ a proper choice of coupling strengths and using spin memory- technique improved. We also analyse the security＂ of the scheme against the cloning-based attack which can be also implemented in spin network and discover that this spin network cloning coincides with the optimal fidelity- achieved by＂ an eavesdropper for entanglement-based cryptography.     

Single Sign-On Under Quantum Cryptography

Single Sign-On (SSO) is an important cryptography mechanism in distributed systems and is implemented in many known systems, such as the famous Kerberos. Quantum cryptography has excellent security properties guaranteed by physical principles and makes great influence on traditional cryptography. In this paper, we combines the SSO mechanism and quantum cryptography together. A SSO solution under quantum cryptography is designed. Through security analysis, we show that this solution has good security properties.     

Reconstruction of high reflectance fiber Bragg grating from noisy data

The inverse scattering problem for fiber Bragg grating reconstruction becomes incorrect with an increasing level of noise in the input data or at a high reflection. The adaptive regularization procedure is proposed to restore the correctness and minimizing the reconstruction error. The proposed method is tested using numerical modeling with the Gaussian statistics of noise.     

Maximum likelihood estimation of structural wave components from noisy data

In this paper, a general framework is developed for determining the underlying parameters of general signal models through the application of maximum likelihood estimation theory for functions whose variables separate. This method extends previous work in sinusoidal and exponential estimation to include models with other functional bases, such as exponential functions with nonconstant amplitudes and Bessel functions. Nonuniform spatial sampling is also possible with this technique. The maximum likelihood method is applied to the identification of wave components along one-dimensional structural elements. Results are given which demonstrate the viability and accuracy of the technique estimating exponential and Bessel function model parameters from noisy simulation data.     

Experimental extraction of secure correlations from a noisy private state

We report experimental generation of a noisy entangled four-photon state that exhibits a separation between the secure key contents and distillable entanglement, a hallmark feature of the recently established quantum theory of private states. The privacy analysis, based on the full tomographic reconstruction of the prepared state, is utilized in a proof-of-principle key generation. The inferiority of distillation-based strategies to extract the key is exposed by an implementation of an entanglement distillation protocol for the produced state.     

Reconstructing bifurcation diagrams from noisy time series using nonlinear autoregressive models

We introduce a formalism for the reconstruction of bifurcation diagrams from noisy time series. The method consists in finding a parametrized predictor function whose bifurcation structure is similar to that of the given system. The reconstruction algorithm is composed of two stages: model selection and bifurcation parameter identification. In the first stage, an appropriate model that best represents all the given time series is selected. A nonlinear autoregressive model with polynomial terms is employed in this study. The identification of the bifurcation parameters from among the many model parameters is done in the second stage. The algorithm works well even for a limited number of time series.     

Iterative Wiener deconvolution based method for phase retrieval from noisy intensities

To retrieve the phase from the noisy measured intensities in the diffraction planes, an iterative Wiener deconvolution based method is proposed. With the same iterative scheme as the iterative angular spectrum method (IAS), the propagation of the optical wave function between the input plane and the diffraction planes is calculated by Wiener deconvolution in this method. The angular spectrum convolution kernel used in the iterative angular spectrum method is incorporated into the Wiener filter. The simulation experiments show that the proposed method can reduce the impact of the noise on the retrieved phase and performed better than the pre-denoising method. Furthermore, the proposed method exhibits great advantage compared to IAS for retrieving the complicated phase distribution from two measured intensities.     

Quantum Overloading Cryptography Using Single-Photon Nonlocality

Using the single-photon nonlocality, we propose a quantum novel overloading cryptography scheme, in which a single photon carries two bits information in one-way quantum channel. Two commutative modes of the single photon, the polarization mode and the spatial mode, are used to encode secret information. Strict time windows are set to detect the impersonation attack. The spatial mode which denotes the existence of photons is noncommutative with the phase of the photon, so that our scheme is secure against photon-number-splitting attack. Our protocol may be secure against individual attack.     

Analytically exact correction scheme for signal extraction from noisy magnitude MR signals

An analytically exact method is proposed to extract the signal intensity and the noise variance simultaneously from noisy magnitude MR signals. This method relies on a fixed point formula of signal-to-noise ratio (SNR) and a correction factor. The correction factor, which is a function of SNR, establishes a fundamental link between the variance of the magnitude MR signal and the variance of the underlying Gaussian noise in the two quadrature channels. A more general but very similar method is developed for parallel signal acquisitions with multiple receiver coils. In the context of MR imaging, the proposed method can be carried out on a pixel-by-pixel basis if the mean and the standard deviation of the magnitude signal are available.