Related papers: Quantum Walks with Entangled Coins
In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the…
Parrondo's paradox, a counterintuitive phenomenon where two losing strategies combine to produce a winning outcome, has been a subject of interest across various scientific fields, including quantum mechanics. In this study, we investigate…
We consider quantum walks on the cycle in the non-stationary case where the `coin' operation is allowed to change at each time step. We characterize, in algebraic terms, the set of possible state transfers and prove that, as opposed to the…
A discrete time quantum walk is considered in which the step lengths are chosen to be either $1$ or $2$ with the additional feature that the walker is persistent with a probability $p$. This implies that with probability $p$, the walker…
The analysis of a physical problem simplifies considerably when one uses a suitable coordinate system. We apply this approach to the discrete-time quantum walks with coins given by $2j+1$-dimensional Wigner rotation matrices (Wigner walks),…
We consider an special dynamics of a quantum walk (QW) on a line. Initially, the walker localized at the origin of the line with arbitrary chirality, evolves to an asymptotic stationary state. In this stationary state a measurement is…
For a discrete time quantum walk (QW) on the $N$-cycle, allowing for decoherence on the coin, we derive a number of new results, including an explicit formula for the position probability distribution. For a QW of this type, we show that…
The evolution of a many-particle system on a one-dimensional lattice, subjected to a quantum walk can cause spatial entanglement in the lattice position, which can be exploited for quantum information/communication purposes. We demonstrate…
Quantum walks are dynamic systems with a wide range of applications in quantum computation and quantum simulation of analog systems, therefore it is of common interest to understand what changes from an isolated process to one embedded in…
The behaviors of one-dimensional quantum random walks are strikingly different from those of classical ones. However, when decoherence is involved, the limiting distributions take on many classical features over time. In this paper, we…
We introduce quantum walks on Cayley graphs of non-Abelian groups. We focus on the easiest case of virtually Abelian groups, and introduce a technique to reduce the quantum walk to an equivalent one on an Abelian group with coin system…
We extend to the gamut of functional forms of the probability distribution of the time-dependent step-length a previous model dubbed Elephant Quantum Walk, which considers a uniform distribution and yields hyperballistic dynamics where the…
In this paper we investigate one dimensional quantum walks with two-step memory, which can be viewed as an extension of quantum walks with one-step memory. We develop a general formula for the amplitudes of the two-step-memory walk with…
We characterize quantumness of the so-called quantum walks (whose dynamics is governed by quantum mechanics) by introducing two computable measures which are stronger than the variance of the walker's position probability distribution. The…
Entanglement is a fundamental resource for many applications in quantum information processing. Here, we investigate how quantum transport in simple quantum graphs, modeled as controlled two-level quantum systems, can be utilized to…
For quantum computation using photons, performing deterministic quantum gate operations is a challenge due to the probabilistic nature of the photon-photon interaction. Encoding qubits in multiple degrees-of-freedom of photons and…
In discrete time, coined quantum walks, the coin degrees of freedom offer the potential for a wider range of controls over the evolution of the walk than are available in the continuous time quantum walk. This paper explores some of the…
Recurrence in the classical random walk is well known and described by the P\'olya number. For quantum walks, recurrence is similarly understood in terms of the probability of a localized quantum walker to return to its origin. Under…
We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…