Quantum Zeno effect in unitary quantum mechanics

Carlo Presilla A, Roberto Onofrio, Ubaldo Tambini

Alexander D Panov

Gershon Kurizki

The quantum Zeno effect (QZE) introduced by Misra and Sudarshan consists in the ability of repeated measurements to inhibit or slow down unitary evolution. Its fundamental status in quantum mechanics has long been firmly established, but its much broader context, in-depth understanding and its applications are growing at a faster pace than ever before. Over the years, there have been several pivotal developments that have made the QZE and related effects the basic paradigms underlying the control of evolution in quantum systems:

Wenqiang Zheng, Dazhi Xu, Xinhua Peng +3 more

We experimentally demonstrate a dynamic fashion of quantum Zeno effect in nuclear magnetic resonance systems. The frequent measurements are implemented through quantum entanglement between the target qubit(s) and the measuring qubit, which dynamically results from the unitary evolution of duration ${\ensuremath{\tau}}_{m}$ due to dispersive coupling. Experimental results testify to the presence of ``the critical measurement time effect,'' that is, the quantum Zeno effect does not occur when ${\ensuremath{\tau}}_{m}$ takes some critical values, even if the measurements are frequent enough. Moreover, we provide an experimental demonstration of an entanglement preservation mechanism based on such a dynamic quantum Zeno effect.

Alexander Hahn, Daniel Klaus Burgarth, Kazuya Yuasa

Abstract Periodic deterministic bang–bang dynamical decoupling and the quantum Zeno effect are known to emerge from the same physical mechanism. Both concepts are based on cycles of strong and frequent kicks provoking a subdivision of the Hilbert space into independent subspaces. However, previous unification results do not capture the case of random bang–bang dynamical decoupling, which can be advantageous to the deterministic case but has an inherently acyclic structure. Here, we establish a correspondence between random dynamical decoupling and the quantum Zeno effect by investigating the average over random decoupling evolutions. This protocol is a manifestation of the quantum Zeno dynamics and leads to a unitary bath evolution. By providing a framework that we call equitability of system and bath, we show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.

Leo Georgy Sapogin