Bath Dynamical Decoupling with a Quantum Channel

TL;DR

This paper extends dynamical decoupling techniques by using quantum channels instead of unitary operations, establishing conditions for effective decoherence suppression and exploring quantum Zeno dynamics with CPTP kicks.

Contribution

It introduces a generalized framework for bath dynamical decoupling using quantum channels and derives conditions for its effectiveness, expanding the theoretical understanding of decoherence control.

Findings

Bath dynamical decoupling works if and only if the quantum channel is ergodic.

CPTP kicks can induce quantum Zeno dynamics without requiring ergodicity.

Spectral properties of ergodic quantum channels are characterized.

Abstract

Bang-bang dynamical decoupling protects an open quantum system from decoherence due to its interaction with the surrounding bath/environment. In its standard form, this is achieved by strongly kicking the system with cycles of unitary operations, which average out the interaction Hamiltonian. In this paper, we generalize the notion of dynamical decoupling to repeated kicks with a quantum channel, which is applied to the bath. We derive necessary and sufficient conditions on the employed quantum channel and find that bath dynamical decoupling works if and only if the kick is ergodic. Furthermore, we study in which circumstances CPTP kicks on a mono-partite quantum system induce quantum Zeno dynamics with its Hamiltonian cancelled out. This does not require the ergodicity of the kicks, and the absence of decoherence-free subsystems is both necessary and sufficient. While the standard unitary dynamical decoupling is essentially the same as the quantum Zeno dynamics, our investigation implies that this is not true any more in the case of CPTP kicks. To derive our results, we prove some spectral properties of ergodic quantum channels, that might be of independent interest. Our approach establishes an enhanced and unified mathematical understanding of several recent experimental demonstrations and might form the basis of new dynamical decoupling schemes that harness environmental noise degrees of freedom.