Zeno subspace in quantum-walk dynamics

TL;DR

This paper explores how frequent measurements in a quantum walk can induce the quantum Zeno effect in position subspace, affecting the walk's dynamics and potential quantum information applications.

Contribution

It demonstrates the conditions under which the quantum Zeno effect occurs in position subspace and discusses its implications for quantum state preservation and multidimensional systems.

Findings

Quantum Zeno effect occurs when measurement frequency exceeds a critical value.

Survival probability at a position can be maintained via frequent measurements.

The effect preserves coin space dynamics and aids quantum state control.

Abstract

We investigate the discrete-time quantum walk evolution under the influence of the periodic measurements in position subspace. The undisturbed survival probability of the particle at the position subspace, $P(0, t)$ is compared with the survival probability after frequent ($n$) measurements at interval $\tau = t/n$, $P(0, \tau)^n$. We show that $P(0, \tau)^n > P(0, t)$ leading to the quantum Zeno effect in the position subspace when a parameter $\theta$ in the quantum coin operations and frequency of measurements is greater than the critical value, $\theta > \theta_{c}$ and $n>n_{c}$. This Zeno effect in the subspace preserves the dynamics in coin Hilbert space of the walk dynamics and has a potential to play a significant role in quantum tasks such as, preserving the quantum state of the particle at any particular position and to understand the Zeno dynamics in a multidimensional system which is highly transient in nature.