Ignorance Is Bliss: General and Robust Cancellation of Decoherence via No-Knowledge Quantum Feedback

Abstract

A "no-knowledge" measurement of an open quantum system yields no information about any system observable; it only returns noise input from the environment. Surprisingly, performing such a noknowledge measurement can be advantageous. We prove that a system undergoing no-knowledge monitoring has reversible noise, which can be canceled by directly feeding back the measurement signal. We show how no-knowledge feedback control can be used to cancel decoherence in an arbitrary quantum system coupled to a Markovian reservoir that is being monitored. Since no-knowledge feedback does not depend on the system state or Hamiltonian, such decoherence cancellation is guaranteed to be general and robust, and can operate in conjunction with any other quantum control protocol. As an application, we show that no-knowledge feedback could be used to improve the performance of dissipative quantum computers subjected to local loss. "More signal, less noise" is the guiding philosophy of experimental science. Increasing measurement sensitivity is a proven strategy for pushing the frontiers of science and technology, yielding improved knowledge and control over nature. However, at the quantum scale physics pushes back by imposing a fundamental limit on the signal-to-noise ratio by virtue of Heisenberg's uncertainty principle [1,2]. Nevertheless, "more signal, less noise" also guides the design of protocols for the measurement and control of quantum systems, such as squeezed state photon [3] and atom [4] interferometry, optimal parameter estimation [5], weak measurement [6], measurement-based feedback control [5,7], and adaptive measurement [8]. In this Letter, we take the unorthodox "no signal, only noise" approach, and consider measurements that are pure noise, and therefore give no knowledge of the quantum state whatsoever. From a quantum control perspective, one intuitively expects such "no-knowledge" measurements to be unworthy of study, since robust feedback control requires at least some (and preferably good) knowledge of the system state. On the contrary, we show that a measurement-based feedback protocol based on no-knowledge monitoring can be used to remove decoherence-the bane of quantum technologyfrom an arbitrary quantum system coupled to a Markovian environment that can be monitored.Although the "no signal, only noise" approach is unorthodox, it has been considered within the context of channel correction. In Refs. [9][10][11], it was proven that coherence could be recovered in a noisy channel provided the conditional evolution was random unitary. Consequently, complete correction is, in principle, possible for systems with dimension d ≤ 3. Furthermore, it was proven that measurements that returned a small amount of knowledge ("little signal, mostly noise") provided a good error correction strategy, and a tradeoff relation between information extraction and correction efficacy was established [12]. Our no-knowledge feedback scheme is consistent with these results; however, it goes several steps further as (1) it concretely ...

Quantum feedback: Theory, experiments, and applications

“…The feedback is thus capable of eliminating the effect of atomic collisions on the linewidth of the laser [182,183]. Continuous-time feedback has also been applied to quantum error correction, a technique that is able to slow the decoherence of unknown quantum states [114,115,[184][185][186][187][188]. By "unknown", we mean that the controller is able to preserve the initial state without knowing what the state is.…”

Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment

“…It is important to remark that the use of continuous measurements and feedback techniques has long been recognized as a useful tool for fighting decoherence and to prepare non-classical quantum states [27,[69][70][71][72][73][74][75]. Our metrological scheme follows this line of thought, but with the great advantage that it is based on continuous monitoring only, without error correction steps (or feedback), differing it from other recent approaches in noisy quantum metrology [21,22].…”

Entanglement-assisted quantum feedback control

“…Remark: The measurement output dy t = DdŴ t in Eq. (18) has the form of no-knowledge measurement [42], which can be used to cancel decoherence. Interestingly, unlike the measurement scheme presented here, the no-knowledge one does not provide any information to the observer; actually for the setup of [42] it can be proven that A is not Hurwitz and the estimation error diverges.…”