Quantum Zeno dynamics: mathematical and physical aspects

Abstract

If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected "quantum Zeno subspace" is called "quantum Zeno dynamics:" for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. We discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. We then analyze some alternative strategies to obtain a Zeno dynamics and show that they are physically equivalent.

52 pages, 10 figures

References in corpus (6)

• Universal dynamical decoherence control of noisy single-and multi-qubit systems
• Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation
• Long-range entanglement generation via frequent measurements
• Distillation of Entanglement between Distant Systems by Repeated Measurements on Entanglement Mediator
• A Simple Scheme to Entangle Distant Qubits from a Mixed State via an Entanglement Mediator
• Estimation of the Repeatedly-Projected Reduced Density Matrix under Decoherence