# Quantum Zeno effect generalized

## TL;DR

This paper generalizes the quantum Zeno effect to open systems, time-dependent dynamics, and general quantum operations, showing how frequent measurements can still inhibit evolution under broader conditions.

## Contribution

It extends the quantum Zeno effect framework to include open systems, time-dependent equations, and general quantum operations, broadening its applicability.

## Key findings

- Frequent measurements can freeze evolution outside an invariant subspace.
- Inside the invariant subspace, evolution follows a modified master equation.
- Spectral gap condition ensures the effectiveness of the Zeno effect in generalized settings.

## Abstract

The quantum Zeno effect, in its original form, uses frequent projective measurements to freeze the evolution of a quantum system that is initially governed by a fixed Hamiltonian. We generalize this effect simultaneously in three directions by allowing open system dynamics, time-dependent evolution equations and general quantum operations in place of projective measurements. More precisely, we study Markovian master equations with bounded generators whose time dependence is Lipschitz continuous. Under a spectral gap condition on the quantum operation, we show how frequent measurements again freeze the evolution outside an invariant subspace. Inside this space the evolution is described by a modified master equation.