One-dimensional quantum walks driven by two-entangled-qubit coins

TL;DR

This paper explores how entanglement between two qubits influences one-dimensional quantum walks, revealing controllable behaviors, self-trapping, perfect transfer, and entropy dynamics based on initial entanglement levels.

Contribution

It introduces a novel quantum walk model driven by two entangled qubits, demonstrating how entanglement controls walk dynamics and properties, including symmetry, transfer speed, and entropy.

Findings

Entanglement enables control over walk behavior and symmetry.

Maximal entanglement leads to highest entropy and distinct walk properties.

Self-trapped behavior and perfect transfer are observed at high velocities.

Abstract

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 walker's state from a classical to standard quantum-walk behavior, and a novel one. Additionally, we report on self-trapped behavior and perfect transfer with highest velocity for the walker. We also show that symmetry of probability density distribution, the most probable place to find the walker and evolution of the entropy are subject to initial entanglement between the qubits. In fact, we confirm that if the two qubits are separable (zero entanglement), entropy becomes minimum whereas its maximization happens if the two qubits are initially maximally entangled. We will make contrast between cases where the entangled qubits are affected by coin operator identically or else, and show considerably different deviation in walker's behavior and its properties.