Related papers: Exploring $2d$ localization with a step dependent …
We investigate the evolution of a discrete-time one-dimensional quantum walk driven by a position-dependent coin. The rotation angle which depends upon the position of a quantum particle parameterizes the coin operator. For different values…
The discrete-time quantum walk is a quantum counterpart of the random walk. It is expected that the model plays important roles in the quantum field. In the quantum information theory, entanglement is a key resource. We use the von Neumann…
We report on the possibility of controlling quantum random walks with a step-dependent coin. The coin is characterized by a (single) rotation angle. Considering different rotation angles, one can find diverse probability distributions for…
Quantum walks, both discrete (coined) and continuous time, form the basis of several recent quantum algorithms. Here we use numerical simulations to study the properties of discrete, coined quantum walks. We investigate the variation in the…
We study the localization properties, energy spectra and coin-position entanglement of the aperiodic discrete-time quantum walks. The aperiodicity is described by spatially dependent quantum coins distributed on the lattice, whose…
The evolution operator of a discrete-time quantum walk involves a conditional shift in position space which entangles the coin and position degrees of freedom of the walker. After several steps, the coin-position entanglement (CPE)…
The conditional shift in the evolution operator of a quantum walk generates entanglement between the coin and position degrees of freedom. This entanglement can be quantified by the von Neumann entropy of the reduced density operator…
We analyze the effect of a simple coin operator, built out of Bell pairs, in a $2d$ Discrete Quantum Random Walk (DQRW) problem. The specific form of the coin enables us to find analytical and closed form solutions to the recursion…
We systematically study the localization effect in discrete-time quantum walks on a honeycomb network and establish the mathematical framework. We focus on the Grover walk first and rigorously derive the limit form of the walker's state,…
Exploiting multi-dimensional quantum walks as feasible platforms for quantum computation and quantum simulation is attracting constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional…
We consider a d-dimensional random quantum walk with site-dependent random coin operators. The corresponding transition coefficients are characterized by deterministic amplitudes times independent identically distributed site-dependent…
Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited…
We investigate the relation between transport properties and entanglement between the internal (spin) and external (position) degrees of freedom in one-dimensional discrete time quantum walks. We obtain closed-form expressions for the…
In this paper, we investigate the enhancement of delocalization and coin-position entanglement in asymmetric discrete-time quantum walks (DTQWs). The asymmetry results from asymmetric coin operations, asymmetric initial states, and…
Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip…
We present a mathematical formalism for the description of unrestricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, two different…
In this work, we use the Shannon informational entropies to study an electron confined in a double quantum dot; we mean the entropy in the space of positions, $S_r$, in the space of momentum, $S_p$, and the total entropy, $S_t = S_r+S_p$.…
We study one-dimensional quantum walk with four internal degrees of freedom resulted from two entangled qubits. We will demonstrate that the entanglement between the qubits and its corresponding coin operator enable one to steer the…
Using the concept of von Neumann entropy, we quantify the information content of the various components of the quantum walk system, including the mutual information between its subsystems (coin and position) and use it to give a precise…
There is a property called localization, which is essential for applications of quantum walks. From a mathematical point of view, the occurrence of localization is known to be equivalent to the existence of eigenvalues of the time evolution…