Quantum Zeno effect and dynamics

TL;DR

This paper explores the quantum Zeno effect, where frequent measurements inhibit system evolution, and introduces a new product formula to characterize the effect and its dynamics for finite-rank projections.

Contribution

It provides a novel characterization of the quantum Zeno effect and dynamics using a new product formula and spectral decay properties of the Hamiltonian.

Findings

Characterization of quantum Zeno effect via spectral decay

New product formula for finite-rank projections

Description of limiting quantum Zeno dynamics

Abstract

If frequent measurements ascertain whether a quantum system is still in a given subspace, it remains in that subspace and a quantum Zeno effect takes place. The limiting time evolution within the projected subspace is called quantum Zeno dynamics. This phenomenon is related to the limit of a product formula obtained by intertwining the time evolution group with an orthogonal projection. By introducing a novel product formula we will give a characterization of the quantum Zeno effect for finite-rank projections, in terms of a spectral decay property of the Hamiltonian in the range of the projections. Moreover, we will also characterize its limiting quantum Zeno dynamics and exhibit its (not necessarily lower-bounded) generator as a generalized mean value Hamiltonian.