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Quantum walks represent an excellent testbed for investigating the interplay between unitary coherent and incoherent dissipative processes. Thanks to photonic quantum interferometers of considerable size, experimental studies could be…
Quantum metrology protocols allow to surpass precision limits typical to classical statistics. However, in recent years, no-go theorems have been formulated, which state that typical forms of uncorrelated noise can constrain the quantum…
Statistics of classical Hamiltonian random walk of particle colliding with atoms of ideal gas is considered from viewpoint of earlier suggested exact pseudo-quantum path integral representation of the problem, and qualitative agreement is…
Surprisingly the looking natural random walk leading to Brownian motion occurs to be often biased in a very subtle way: usually refers to only approximate fulfillment of thermodynamical principles like maximizing uncertainty. Recently, a…
With the increasing crossover between quantum information and machine learning, quantum simulation of neural networks has drawn unprecedentedly strong attention, especially for the simulation of associative memory in Hopfield neural…
We address continuous-time quantum walks on graphs in the presence of time- and space-dependent noise. Noise is modeled as generalized dynamical percolation, i.e. classical time-dependent fluctuations affecting the tunneling amplitudes of…
The quantum wave-function of a massive particle with small initial uncertainties (consistent with the uncertainty relation) is believed to spread very slowly, so that the dynamics is deterministic. This assumes that the classical motions…
This paper is concerned with the generation of Gaussian invariant states in cascades of open quantum harmonic oscillators governed by linear quantum stochastic differential equations. We carry out infinitesimal perturbation analysis of the…
We investigate the transport properties of open quantum chaotic systems in the semiclassical limit. We show how the transmission spectrum, the conductance fluctuations, and their correlations are influenced by the underlying chaotic…
In quantum sensing and metrology, an important class of measurement is the continuous linear measurement, in which the detector is coupled to the system of interest linearly and continuously in time. One key aspect involved is the quantum…
We employ stochastic quantization for a self-interacting nonminimal massive scalar field in curved spacetime. The covariant background field method and local momentum space representation are used to obtain the Euclidean correlation…
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a…
Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with…
Rules for quantizing the walker+coin parts of a classical random walk are provided by treating them as interacting quantum systems. A quantum optical random walk (QORW), is introduced by means of a new rule that treats quantum or classical…
The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…
We study the dynamics of a generalization of quantum coin walk on the line which is a natural model for a diffusion modified by quantum or interference effects. In particular, our results provide surprisingly simple explanations to…
An explicit formula of the Hamiltonians generating one-dimensional discrete-time quantum walks is given. The formula is deduced by using the algebraic structure introduced previously. The square of the Hamiltonian turns out to be an…
Discrete-time quantum walks are known to exhibit exotic topological states and phases. Physical realization of quantum walks in a noisy environment may destroy these phases. We investigate the behavior of topological states in quantum walks…
We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…
We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup defined in Quantum Probability via quantum stochastic differential equations. Given a homogeneous Markov chain in continuous time in a finite…