Related papers: Quantum White Noise and the Master Equation for Ga…
With the use of Hida's white noise space theory space theory and spaces of stochastic distributions, we present a detailed analytic continuation theory for classes of Gaussian processes, with focus here on Brownian motion. For the latter,…
We approach the theoretical problem of compressing a signal dominated by Gaussian noise. We present expressions for the compression ratio which can be reached, under the light of Shannon's noiseless coding theorem, for a linearly quantized…
In this paper, we propose a quantized learning equation with a monotone increasing resolution of quantization and stochastic analysis for the proposed algorithm. According to the white noise hypothesis for the quantization error with dense…
Within the framework of the Accardi-Fagnola-Quaegebeur (AFQ) representation free calculus of \cite{b}, we consider the problem of controlling the size of a quantum stochastic flow generated by a unitary stochastic evolution affected by…
We present a method, based on the Keldysh formalism, for deriving stochastic master equations that describe the non-Markovian dynamics of a quantum system coupled to a Gaussian environment. This approach yields a compact expression for the…
A two-step optimization is proposed to represent an arbitrary quantum state to a desired accuracy with the least number of gaussians in phase space. The Husimi distribution of the quantum state provides the information to determine the…
The squeezed state is used to study the one-dimensional quantum mechanical Frenkel Kontorova model. A set of coupled equations for the particle's expectation value and the fluctuations for the ground state are derived. It is shown that…
This paper investigates the behavior of two fundamental types of multipartite entangled states, namely GHZ(3) and W(3) states under Gaussian-distributed amplitude perturbations and White noise model. The Uhlmann-Jozsa fidelity is taken to…
We illustrate a counter-intuitive effect of an additive stochastic force, which acts independently on each element of an ensemble of globally coupled oscillators. We show numerically and semi-analytically that a very small white noise is…
Covariant stochastic partial differential equations are studied in any dimension. A special class of such equations is selected and it is proven that the solutions can be analytically continued to Minkowski space-time yielding tempered…
In this paper we consider the two-dimensional stochastic Gross-Pitaevskii equation, which is a model to describe Bose-Einstein condensation at positive temperature. The equation is a complex Ginzburg-Landau equation with a harmonic…
Quantum systems are unavoidably open to their surrounding degrees of freedom. The theory of open quantum systems is thus crucial to understanding the fluctuations, dissipation, and decoherence of a quantum system of interest. Typically, the…
In this article, we consider the stochastic wave equation in spatial dimension $d=1$, with linear term $\sigma(u)=u$ multiplying the noise. This equation is driven by a Gaussian noise which is white in time and fractional in space with…
We study a generalized notion of two-mode squeezing for the Stokes and anti-Stokes fields in a model of a cavity Raman laser, which leads to a significant reduction in decoherence or quantum noise. The model comprises a loss-less cavity…
We examine the quantum states produced through parametric amplification with internal quantum noise. The internal diffusion arises by coupling both modes of light to a reservoir for the duration of the interaction time. The Wigner function…
The report presents a general approach for estimating quantum information technologies by means of fuzzy quantum measurements. The developed methods are used for precision reconstruction of quantum states under conditions of significant…
With the successes of the Laser Interferometer Gravitational-wave Observatory, we anticipate increased interest in working with squeezed states in the undergraduate and graduate quantum-mechanics classroom. Because squeezed-coherent states…
The two-mode relative phase associated with Gaussian states plays an important role in quantum information processes in optical, atomic and electronic systems. In this work, the origin and structure of the two-mode relative phase in pure…
We obtain the solutions of the generic bilinear master equation for a quantum oscillator with constant coefficients in the Gaussian form. The well-behavedness and positive semidefiniteness of the stationary states could be characterized by…
We investigate an optical scheme to conditionally engineer quantum states using a beam splitter, homodyne detection and a squeezed vacuum as an ancillar state. This scheme is efficient in producing non-Gaussian quantum states such as…