Effects of time delay in no-knowledge quantum feedback control

Abstract

The no-knowledge quantum feedback, introduced in Phys. Rev. Lett., 113, 020407 (2014), is a measurement-based feedback protocol for decoherence suppression in a quantum system coupled to noisy environment. By continuously measuring the environmental noise, without directly gathering any information about the system, the decoherence effect can be suppressed by feeding back quantum controls proportional to the measured signal. In the original work, the feedback control was assumed instantaneous, leading to perfect cancellation of noise backaction on the quantum system. However, the instantaneous feedback is difficult to achieve in practice, and close-loop feedback protocols are always associated with finite delayed time. Therefore, in this work, we consider the effects of the delay between the time at which the measurement signal is acquired and the time that such signal is fed back to the system. We investigate the problem with an example of a two-level system (qubit) coupled to a Markovian reservoir, via a Hermitian coupling operator, where a homodyne detection is used to measure the environmental noise. We numerically simulate quantum stochastic trajectories of the qubit and analyse their averaged dynamics. We find that the feedback control with time delay can either enhance or reduce the decoherence effects, depending on whether the delayed time is in-phase or out-of-phase with the unitary dynamics of the qubit system.

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

“…In order to analyze the effect of delay time systematically, we implement the discrete-time operational approach for continuous quantum trajectory with feedback delay [22] and derive analytical solutions (whenever possible) for the system's average dynamics. The discretetime operational approach for quantum trajectories has been used in numerical simulations [23][24][25] and in processing measurement records from experiments [26][27][28], in order to reduce numerical errors from a finite-time resolution.…”

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

“…In order to analyze the effect of delay time systematically, we implement the discrete-time operational approach for continuous quantum trajectory with feedback delay [21] and derive analytical solutions (whenever possible) for the system's average dynamics. The discretetime operational approach for quantum trajectories has been used in numerical simulations [22][23][24] and in processing measurement records from experiments [25][26][27], in order to reduce numerical errors from a finite-time resolution.…”