Tunneling effects in a one-dimensional quantum walk

TL;DR

This paper studies how position decoherence caused by tunneling affects a one-dimensional quantum walk, showing that quantum features like variance and entanglement are preserved under this noise type, unlike coin decoherence.

Contribution

It provides an explicit expression for the probability distribution of a decoherent quantum walk considering tunneling effects, highlighting the robustness of quantum properties.

Findings

Quantum behavior persists under tunneling decoherence.

Quadratic variance dependency remains in the presence of tunneling noise.

Tunneling decoherence smooths the probability distribution without destroying quantum features.

Abstract

In this article we investigate the effects of shifting position decoherence, arisen from the tunneling effect in the experimental realization of the quantum walk, on the one-dimensional discreet time quantum walk. We show that in the regime of this type of noise the quantum behavior of the walker does not fade, in contrary to the coin decoherence for which the walker undergos the quantum-to-classical transition even for weak noise. Particularly, we show that the quadratic dependency of the variance on the time and also the coin-position entanglement, i.e. two important quantum aspects of the coherent quantum walk, are preserved in the presence of tunneling decoherence. Furthermore, we present an explicit expression for the probability distribution of decoherent one-dimensional quantum walk in terms of the corresponding coherent probabilities, and show that this type of decoherence smooths the probability distribution.