Quantum Zeno Effect of General Quantum Operations

TL;DR

This paper demonstrates that the quantum Zeno effect applies broadly to any frequent quantum operations, influencing the evolution of quantum states and operators under continuous measurement or operation regimes.

Contribution

It generalizes the quantum Zeno effect to all quantum measurements and operations, providing a unified framework for understanding their impact on quantum dynamics.

Findings

Quantum Zeno effect occurs for any frequent quantum measurements or operations.

Measurement-invariant states evolve under an effective Hamiltonian.

Selective measurements cause stochastic state changes, but some operators follow effective dynamics.

Abstract

In this paper, we show that the quantum Zeno effect occurs for any frequent quantum measurements or operations. As a result of the Zeno effect, for non-selective measurements (or trace preserving completely positive maps), the evolution of a measurement invariant state is governed by an effective Hamiltonian defined by the measurements and the free-evolution Hamiltonian. For selective measurements, the state may change randomly with time according to measurement outcomes, while some physical quantities (operators) still evolve as the effective dynamics.