Quantum Zeno effect generalized

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.

9 pages; based on Bachelor's thesis of first author

References in corpus (6)

• Quantum Zeno dynamics: mathematical and physical aspects
• Quantum Zeno Dynamics from General Quantum Operations
• Generalized Adiabatic Theorem and Strong-Coupling Limits
• Quantum evolution in the stroboscopic limit of repeated measurements
• Quantum Zeno effect for open quantum systems
• Generalized quantum Zeno dynamics and ergodic means

Cited by in corpus (9)

• Quantum Zeno effect for open quantum systems
• Eternal Adiabaticity
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect
• Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions
• On Strong Bounds for Trotter and Zeno Product Formulas with Bosonic Applications
• Product formulas in the framework of mean ergodic theorems
• Revisiting Kinetic Monte Carlo Algorithms for Time-dependent Processes: from open-loop control to feedback control
• Convergence Rates for the Trotter Splitting for Unbounded Operators
• Bath Dynamical Decoupling with a Quantum Channel