Related papers: Uncertainty relation between detection probability…
It was recently proposed to use extra-galactic point sources to constrain space-time quantum fluctuations in the universe. In these proposals, the fundamental "fuzziness" of distance caused by space-time quantum fluctuations have been…
Recent progress in electro-optic sampling has allowed direct access to the fluctuations of the electromagnetic ground state. Here, we present a theoretical formalism that allows for an in-depth characterisation and interpretation of such…
Fluctuations are ubiquitous in nature. They are one of the fundamental building blocks of quantum mechanics and are responsible for a wide variety of phenomena in many areas of physics, ranging from biology to cosmology. Far from any…
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…
We study the Ergodic Properties of Random Walks in stationary ergodic environments without uniform ellipticity under a minimal assumption. There are two main components in our work. The first step is to adopt the arguments of Lawler to…
We formulate a discrete two-state stochastic process with elementary rules that give rise to Born statistics and reproduce the probabilities from the Schr\"odinger equation under an associated Hamiltonian matrix, which we identify. We…
The primary ingredients of reality are the universal quantum fields, which fluctuate persistently, spontaneously, and randomly. The general perception of the scientific community is that these quantum fluctuations are due to the uncertainty…
Thermodynamic uncertainty relations unveil useful connections between fluctuations in thermal systems and entropy production. This work extends these ideas to the disparate field of \textit{zero temperature} quantum mesoscopic physics where…
Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element only. We show…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
The problem investigated in this paper is einselection, i. e. the selection of mutually exclusive quantum states with definite probabilities through decoherence. Its study is based on a theory of decoherence resulting from the projection…
Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…
According to the inflationary scenario for the very early Universe, all inhomogeneities in the Universe are of genuine quantum origin. On the other hand, looking at these inhomogeneities and measuring them, clearly no specific quantum…
We introduce a class of nearest-neighbor integer random walks in random and non-random media, which includes excited random walks considered in the literature. At each site the random walker has a drift to the right, the strength of which…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
Computing the reachability probability in infinite state probabilistic models has been the topic of numerous works. Here we introduce a new property called \emph{divergence} that when satisfied allows to compute reachability probabilities…
The probability densities of work that can be exerted on a quantum system initially staying in thermal equilibrium are constrained by the fluctuation relations of Jarzynski and Crooks, when the work is determined by two projective energy…
We address entropic uncertainty relations between time and energy or, more precisely, between measurements of an observable $G$ and the displacement $r$ of the $G$-generated evolution $e^{-ir G}$. We derive lower bounds on the entropic…
Quantum walks underlie an important class of quantum computing algorithms, and represent promising approaches in various simulations and practical applications. Here we design stroboscopically monitored quantum walks and their subsequent…
Multilayer network is a potent platform which paves a way to study the interactions among entities in various networks with multiple types of relationships. In this study, the dynamics of discrete-time quantum walk on a multilayer network…