Quantum Zeno effect and 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.

15 pages, 1 figure

References in corpus (5)

• Quantum Zeno dynamics: mathematical and physical aspects
• Product formula related to quantum Zeno dynamics
• Zeno product formula revisited
• Zeno Dynamics in Quantum Statistical Mechanics
• Zeno Dynamics of von Neumann Algebras

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• Quantum Zeno Dynamics from General Quantum Operations
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• Unification of quantum Zeno-anti Zeno effects and parity-time symmetry breaking transitions
• Eternal Adiabaticity
• Experimental protection against evolution of states in a subspace via a super-Zeno scheme on an NMR quantum information processor
• Universal Control Induced by Noise
• Tunneling in Polymer Quantization and the Quantum Zeno Effect
• Noise-induced distributed entanglement in atom-cavity-fiber system
• Non-Markovian noise that cannot be dynamically decoupled by periodic spin echo pulses
• Nonexponential decay of Feshbach molecules
• Generalized Product Formulas and Quantum Control
• Large-time limit of the quantum Zeno effect
• Quantum cavities with alternating boundary conditions
• Kick and fix: the roots of quantum control
• The semiclassical limit of a quantum Zeno dynamics
• Truncated quantum observables and their semiclassical limit
• Finite-size scalings in measurement-induced dynamical phase transition
• The quantum Zeno and anti-Zeno effects with strong system-environment coupling
• Free dilations of families of ${\mathcal{C}}_0$-semigroups and applications to evolution families
• Observation of the Quantum Zeno Effect on a NISQ Device
• The quantum Zeno and anti-Zeno effects with non-selective measurements