Time-delayed quantum feedback and incomplete decoherence suppression with no-knowledge measurement

TL;DR

This paper investigates how time delays in no-knowledge quantum feedback affect decoherence suppression, revealing that delays can either hinder or enhance decoherence control depending on system dynamics.

Contribution

It extends previous no-knowledge feedback work by analyzing the impact of realistic feedback delays on decoherence suppression in quantum systems.

Findings

Delayed feedback can degrade decoherence suppression.

Non-commuting dynamics can lead to either suppression or amplification of decoherence.

Analytical and numerical results quantify delay effects on a two-level system.

Abstract

The no-knowledge quantum feedback was proposed by Szigeti et al., Phys. Rev. Lett. 113, 020407 (2014), as a measurement-based feedback protocol for decoherence suppression for an open quantum system. By continuously measuring environmental noises and feeding back controls on the system, the protocol can completely reverse the measurement backaction and therefore suppress the system's decoherence. However, the complete decoherence cancellation was shown only for the instantaneous feedback, which is impractical in real experiments. Therefore, in this work, we generalize the original work and investigate how the decoherence suppression can be degraded with unavoidable delay times, by analyzing non-Markovian average dynamics. We present analytical expressions for the average dynamics and numerically analyze the effects of the delayed feedback for a coherently driven two-level system, coupled to a bosonic bath via a Hermitian coupling operator. We also find that, when the qubit's unitary dynamics does not commute with the measurement and feedback controls, the decoherence rate can be either suppressed or amplified, depending on the delay time.