Decoherence models for discrete-time quantum walks and their application to neutral atom experiments

Abstract

We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum-walk experiments realized with neutral atoms walking in an optical lattice. From the measured spatial distributions, we determine with good precision the amount of decoherence per step, which provides a quantitative indication of the quality of our quantum walks. In particular, we find that spin decoherence is the main mechanism responsible for the loss of coherence in our experiment. We also find that the sole observation of ballistic-instead of diffusive-expansion in position space is not a good indicator of the range of coherent delocalization. We provide further physical insight by distinguishing the effects of short-and long-time spin dephasing mechanisms. We introduce the concept of coherence length in the discrete-time quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasi-stationary dephasing does not modify the local properties of the quantum walk, but instead affects spatial coherences. For a visual representation of decoherence phenomena in phase space, we have developed a formalism based on a discrete analogue of the Wigner function. We show that the effects of spin and spatial decoherence differ dramatically in momentum space.

Atomic “bomb testing”: the Elitzur–Vaidman experiment violates the Leggett–Garg inequality

“…Besides producing a rigorous violation of the Leggett-Garg inequality for a pseudo-spin-1/2 particle, our results show that the correlation function K can be interpreted, from the point of view quantum theory, as a quantum witness of superposition states, and employed to study decoherenceone of the most basic mechanisms affecting atoms trapped in optical potentials [41]. Fig.…”

Controlling quantum random walk with a step-dependent coin

“…To do so, we consider the walks with decoherence. It is a well established concept that depending on the amount of decoherence in QW, system's behavior could range from purely quantum like to classical one [21,73,48]. There are different methods to include decoherence in QW.…”

“…Inclusion of decoherence results into losing the unitary nature of the process. Therefore, one should use density operator formalism to address the nonunitary evolution of the walk at each step given by [21,73,48]     r r r r…”

“…It should be noted that if one considers ¹ s 0, the fitting would even improve further. For further comparison between SDC walk with rotation angle of θ=2π/5 and decoherent one, please compare figure B2(6) with figure 2 in [73].…”

Relativistic Wigner Function for Quantum Walks

“…If one follows the standard procedure adopted for Dirac fermions [36][37][38], one should first build a relativistic Wigner function for DTQWs and then describe the phase-space dynamics by the transport equation obeyed by that function. Until now, the only Wigner functions that have been considered for DTQWs [39][40][41][42] are non relativistic [43]. Thus, these function and the equation they obey do not coincide, at the continuous limit, with the usual Wigner function and phase-space transport equation for Dirac fermions.…”