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QUANTUM ZENO SUBSPACES AND DYNAMICAL SUPERSELECTION RULES

Paolo Facchi A, Saverio Pascazio

Published Jul 4, 2002• 8 citations
OpenAlex

Abstract

A profound consequence of the quantum Zeno effect is the partitioning of the total Hilbert space into quantum Zeno subspaces, among which any transition is hindered. Such a phenomenon can be due to frequent nonselective measurements, frequent unitary kicks or strong continuous coupling. Its practical relevance for halting decoherence is discussed and the problem of timescales is considered.

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1 Quantum Zeno dynamics and quantum Zeno subspaces ∗

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A quantum Zeno dynamics can be obtained by means of frequent measurements, frequent unitary kicks or a strong continuous coupling and yields a partition of the total Hilbert space into quantum Zeno subspaces, among which any transition is hindered. We focus on the “continuous ” version of the quantum Zeno effect and look at several interesting examples. We first analyze these examples in practical terms, towards applications, then propose a novel experiment. 1

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QUANTUM ZENO EFFECT, ADIABATICITY AND DYNAMICAL SUPERSELECTION RULES

Paolo Facchi A

The evolution of a quantum system undergoing very frequent measurements takes place in a proper subspace of the total Hilbert space (quantum Zeno effect). When the measuring apparatus is included in the quantum description, the Zeno effect becomes a pure consequence of the dynamics. We show that for continuous measurement processes the quantum Zeno evolution derives from an adiabatic theorem. The system is forced to evolve in a set of orthogonal subspaces of the total Hilbert space and a dynamical superselection rule arises. The dynamical properties of this evolution are investigated and several examples are considered. 1

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A profound consequence of the quantum Zeno effect is the partitioning of the total Hilbert space into quantum Zeno subspaces, among which any transition is hindered. Such a phenomenon can be due to frequent nonselective measurements, frequent unitary kicks or strong continuous coupling. Its practical relevance for halting decoherence is discussed and the problem of timescales is considered.
The quantum Zeno evolution of a quantum system takes place in a proper subspace of the total Hilbert space. The physical and mathematical features of the "Zeno subspaces" depend on the measuring apparatus: when this is included in the quantum description, the Zeno effect becomes a mere consequence of the dynamics and, remarkably, can be cast in terms of an adiabatic theorem, with a dynamical superselection rule. We look at several examples and focus on quantum computation and decoherence-free subspaces.
The evolution of a quantum system undergoing very frequent measurements takes place in a proper subspace of the total Hilbert space (quantum Zeno effect). When the measuring apparatus is included in the quantum description, the Zeno effect becomes a pure consequence of the dynamics. We show that for continuous measurement processes the quantum Zeno evolution derives from an adiabatic theorem. The system is forced to evolve in a set of orthogonal subspaces of the total Hilbert space and a dynamical superselection rule arises. The dynamical properties of this evolution are investigated and several examples are considered.
The evolution of a quantum system undergoing very frequent measurements takes place in a proper subspace of the total Hilbert space (quantum Zeno effect). When the measuring apparatus is included in the quantum description, the Zeno effect becomes a pure consequence of the dynamics. We show that for continuous measurement processes the quantum Zeno evolution derives from an adiabatic theorem. The system is forced to evolve in a set of orthogonal subspaces of the total Hilbert space and a dynamical superselection rule arises. The dynamical properties of this evolution are investigated and several examples are considered. 1