Zeno subspace in quantum-walk dynamics

Details Zeno subspace in quantum-walk dynamics Zeno subspace in quantum-walk dynamics

2010-07-08

arxiv.org/abs/1007.1303v3

Phys. Rev. A 82, 052108 (2010)

Physics

Quantum Physics

5 pages, 5 figures, Published version

Scientific paper

10.1103/PhysRevA.82.052108

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.

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