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The strength of classical correlations is subject to certain constraints, commonly known as Bell inequalities. Violation of these inequalities is the manifestation of nonlocality---displayed, in particular, by quantum mechanics, meaning…
It is shown that the vacuum state of weakly interacting quantum field theories can be described, in the Heisenberg picture, as a linear combination of randomly distributed incoherent paths that obey classical equations of motion with…
We investigate the genuinely quantum features of continuous-time quantum walks by combining a single-time and a multi-time quantifier of nonclassicality. On the one hand, we consider the quantum-classical dynamical distance…
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems…
Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…
We explore the impact of long-range memory on the properties of a family of quantum walks in a one-dimensional lattice and discrete time, which can be understood as the quantum version of the classical "Elephant Random Walk" non-Markovian…
We investigate quantum superposition effects in two-dimensional quantum walks of identical particles with different statistics under particle exchange, starting from various different initial configurations. To characterize interparticle…
Quantum walks have been shown to be fruitful tools in analysing the dynamic properties of quantum systems. This article proposes to use quantum walks as an approach to Quantum Neural Networks (QNNs). QNNs replace binary McCulloch-Pitts…
We generalize the quantum random walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich variety of possible wave function…
Light beams offer many degrees of freedom to be explored in discrete and continuous domains. In addition to the possibility of entangling photons in these many degrees of freedom, it makes light a very useful and versatile tool for quantum…
We introduce an analytically treatable spin decoherence model for quantum walk on a line that yields the exact position probability distribution of an unbiased classical random walk at all-time scales. This spin decoherence model depicts a…
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…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
Experimentally, certain degrees of freedom may appear classical because their quantum fluctuations are smaller than the experimental error associated with measuring them. An approximation to a fully quantum theory is described in which the…
We consider two independent quantum walks on separate lines augmented by partial or full swapping of coins after each step. For classical random walks, swapping or not swapping coins makes little difference to the random walk…
Many disordered systems show a superdiffusive dynamics, intermediate between the diffusive one, typical of a classical stochastic process, and the so called ballistic behaviour, which is generally expected for the spreading in a quantum…
Quantum Stochastic Walks (QSW) allow for a generalization of both quantum and classical random walks by describing the dynamic evolution of an open quantum system on a network, with nodes corresponding to quantum states of a fixed basis. We…
Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after (i) finding that average dynamics of a classical particle in strong inhomogeneous…
We define quantum-like probabilistic behaviour as behaviour which is impossible to describe by using the classical probability model. We discuss the conjecture that cognitive behaviour is quantum-like. There is presented the scheme for an…
Somewhat surprisingly, quantum features can be extracted from a classical bath. For this, we discuss a sample of three-level atoms in ladder configuration interacting only via the surrounding bath, and show that the fluorescence light…