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arXiv:quant-ph/0404058 · Physical Review A

Steering distillation processes through quantum Zeno dynamics

Benedetto Militello, Hiromichi Nakazato, Antonio Messina

Published Mar 8, 2005• 11 citations
arXivHTMLPDF

Abstract

A quantum system in interaction with a repeatedly measured one undergoes a nonunitary time evolution and is pushed into a subspace substantially determined by the two-system coupling. The possibility of suitably modifying such an evolution through quantum Zeno dynamics (i.e., the generalized quantum Zeno effect) addressing the system toward an a priori decided target subspace is illustrated. Applications and their possible realizations in the context of trapped ions are also discussed.

DOI
10.1103/physreva.71.032102

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A quantum system in interaction with a repeatedly measured one undergoes a nonunitary time evolution and is pushed into a subspace substantially determined by the two-system coupling. The possibility of suitably modifying such an evolution through quantum Zeno dynamics (i.e., the generalized quantum Zeno effect) addressing the system toward an a priori decided target subspace is illustrated. Applications and their possible realizations in the context of trapped ions are also discussed.
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 bounded from below) generator as a generalized mean value Hamiltonian.
The evolution of a quantum system undergoing very frequent measurements takes place in a subspace of the total Hilbert space (quantum Zeno effect). The dynamical properties A quantum system, prepared in a state that does not belong to an eigenvalue of its total Hamiltonian, starts to evolve quadratically in time [1, 2]. This behavior leads to the so-called quantum Zeno phenomenon: by performing frequent measurements on the system, in order to check whether it is still in its initial state, one can “slow
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.
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.
Quantum Zeno Dynamics restricts the evolution of a system in a tailorable subspace of the Hilbert space by repeated measurements of a proper observable. This restricted dynamics can be counterintuitive and lead to the generation of interesting nonclassical states. We describe an experiment implementing the Zeno dynamics in an atomic Rydberg level manifold, and we propose an implementation in the cavity quantum electrodynamics context. Both systems open promising perspectives for quantum-enabled metrology and decoherence studies.