Zeno subspace in quantum-walk dynamics
C. M. Chandrashekar · Physical Review A · 2010
We investigate discrete-time quantum-walk evolution under the influence of 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 $\ensuremath{\tau}=t/n$, $P(0,\ensuremath{\tau}){}^{n}$. We show that $P(0,\ensuremath{\tau}){}^{n}>P(0,t)$ leads to the quantum Zeno effect in position subspace when a parameter $\ensuremath{\theta}$ in the quantum coin operations and frequency of measurements is greater than the critical value, $\ensuremath{\theta}>{\ensuremath{\theta}}_{c}$ and $n>{n}_{c}$. This Zeno effect in the subspace preserves the dynamics in coin Hilbert space of the walk dynamics and has the 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 that is highly transient in nature.