Zeno subspace in quantum-walk dynamics

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.

5 pages, 5 figures, Published version

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Cited by in corpus (1)

• Survival probability in a one-dimensional quantum walk on a trapped lattice