Unification of dynamical decoupling and the quantum Zeno effect

Abstract

We unify the quantum Zeno effect (QZE) and the "bang-bang" (BB) decoupling method for suppressing decoherence in open quantum systems: in both cases strong coupling to an external system or apparatus induces a dynamical superselection rule that partitions the open system's Hilbert space into quantum Zeno subspaces. Our unification makes use of von Neumann's ergodic theorem and avoids making any of the symmetry assumptions usually made in discussions of BB. Thus we are able to generalize BB to arbitrary fast and strong pulse sequences, requiring no symmetry, and to show the existence of two alternatives to pulsed BB: continuous decoupling, and pulsed measurements. Our unified treatment enables us to derive limits on the efficacy of the BB method: we explicitly show that the inverse QZE implies that BB can in some cases accelerate, rather than inhibit, decoherence.

Protecting entanglement from decoherence using weak measurement and quantum measurement reversal

“…The decoherence-free subspace, however, requires the interaction Hamiltonian to have an appropriate symmetry, which might not always be present. The quantum Zeno effect may also be used to suppress decoherence 18,19 as well as to generate entanglement 20 under some specific situations.Our scheme for protecting entanglement from decoherence is based on the fact that weak quantum measurement can be reversed. The reversibility of weak quantum measurement was originally discussed in the context of quantum error correction 21 and was demonstrated for a single superconducting qubit and a single photonic qubit [22][23][24] .…”

“…The decoherence-free subspace, however, requires the interaction Hamiltonian to have an appropriate symmetry, which might not always be present. The quantum Zeno effect may also be used to suppress decoherence 18,19 as well as to generate entanglement 20 under some specific situations.…”

Zeno dynamics and constraints

“…Some mechanisms are actually being proposed, based on the so-called "bang-bang" evolutions and their generalization, quantum dynamical decoupling [33]. Although "bang-bang" techniques in classical control theory are know to engineers since long ago [34], their introduction as a quantum control and their unification with the basic ideas underlying the quantum Zeno effect are quite recent [35]. In particular, the decoherencefree subspaces are the dynamically generated quantum Zeno subspaces [7] within which the dynamics is far from being trivial, as has been discussed in this article.…”

Three Different Manifestations of the Quantum Zeno Effect

“…In this section we further elaborate on this issue, obtaining the QZE by means of a generic sequence of frequent instantaneous unitary processes, that need not be spectral decompositions. We will only give the main results, as additional details and a complete proof, which is related to von Neumann's ergodic theorem [15], can be found in [9]. Consider the dynamics of a quantum system Q undergoing N "kicks" U kick (instantaneous unitary transformations) in a time interval t…”

“…2 with general (projective) measurements, then extend in Sect. 3 the notion of QZE to the case of unitary kicks [9] and finally discuss in Sect. 4 (unitary) continuous interactions [10].…”