Effects Of Noise Perturbations Research Articles

Dynamical fidelity susceptibility of decoherence-free subspaces

In idealized models of a quantum register and its environment, quantum information can be stored indefinitely by encoding it into a decoherence-free subspace (DFS). Nevertheless, perturbations to the idealized register-environment coupling will cause decoherence in any realistic setting. Expanding a measure for state preservation, the dynamical fidelity, in powers of the strength of the perturbations, we prove stability to linear order is a generic property of quantum state evolution. The effect of noise perturbation is quantified by a concise expression for the strength of the quadratic, leading order, which we define as the dynamical fidelity susceptibility of DFSs. Under the physical restriction that noise acts on the register $k$-locally, this susceptibility is bounded from above by a polynomial in the system size. These general results are illustrated by two physically relevant examples. Knowledge of the susceptibility can be used to increase coherence times of future quantum computers.

Synaptic efficacy shapes resource limitations in working memory

Working memory (WM) is limited in its temporal length and capacity. Classic conceptions of WM capacity assume the system possesses a finite number of slots, but recent evidence suggests WM may be a continuous resource. Resource models typically assume there is no hard upper bound on the number of items that can be stored, but WM fidelity decreases with the number of items. We analyze a neural field model of multi-item WM that associates each item with the location of a bump in a finite spatial domain, considering items that span a one-dimensional continuous feature space. Our analysis relates the neural architecture of the network to accumulated errors and capacity limitations arising during the delay period of a multi-item WM task. Networks with stronger synapses support wider bumps that interact more, whereas networks with weaker synapses support narrower bumps that are more susceptible to noise perturbations. There is an optimal synaptic strength that both limits bump interaction events and the effects of noise perturbations. This optimum shifts to weaker synapses as the number of items stored in the network is increased. Our model not only provides a circuit-based explanation for WM capacity, but also speaks to how capacity relates to the arrangement of stored items in a feature space.

Fully phase-based encryption using fractional order Fourier domain random phase encoding: error analysis

The performance of a fully phase-based encryption system is analyzed. The encryption is done using a double random fractional Fourier domain random phase encoding technique. The input amplitude data to be encrypted are binary text and a grayscale image of Lena. We study the tolerance to data loss and binarization of the encrypted data/image. The effects of noise perturbations on the encrypted data are also studied. To evaluate the quality of the recovered image, the mean-square error is used as a metric to compare the recovered image with the original input image. Results of computer simulation are presented for analysis.

Error-reduction techniques and error analysis for fully phase- and amplitude-based encryption

The performance of fully phase- and amplitude-based encryption processors is analyzed. The effects of noise perturbations on the encrypted information are considered. A thresholding method of decryption that further reduces the mean-squared error (MSE) for the fully phase- and amplitude-based encryption processes is provided. The proposed thresholding scheme significantly improves the performance of fully phase- and amplitude-based encryption, as measured by the MSE metric. We obtain analytical MSE bounds when thresholding is used for both decryption methods, and we also present computer-simulation results. These results show that the fully phase-based method is more robust. We also give a formal proof of a conjecture about the decrypted distribution of distorted encrypted information. This allows the analytical bounds of the MSE to be extended to more general non-Gaussian, nonadditive, nonstationary distortions. Computer simulations support this extension.

Noise perturbations of a non-linear system with multiple steady states

We examine the effects of small white Gaussian noise perturbations on a harmonically forced Duffing oscillator. For specific values of the parameters, the noise-free system admits two coexisting steady-state attractors. The presence of noise induces transitions from one attractor to the other, however small the noise intensity may be. As a first step, the equation of motion is transformed into a system of stochastic differential equations for the slowly varying van der Pol variables, by assuming that the predominant frequency of response is that of the forcing term. The condition for bistability, the stable fixed points and the separatrix defining the domains of attraction are then examined. In the second step, the effects of noise perturbations on the system are analyzed by determining the steady-state probability density of the fluctuations of the response, as well as the probabilities of escape from one attractor to the other. The latter are found by determination of the expected times of first-passage to the separatrix starting from a point in the domain of attraction of each stable state. This analysis is done in the limit of small damping and small noise intensity by use of an averaging scheme which reduces the dimensionality of the problem from two to one; this yields valuable information about the relative stability of the stable states. The obtained theoretical results are supported by digital simulation data. The analytical theory gives good agreement even for large noise.

Effect of noise perturbation on parametric resonance in a ring laser

Effect of noise perturbation on parametric resonance in a ring laser