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Deterministic Equations for Feedback Control of Open Quantum Systems
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Feedback control in open quantum dynamics is crucial for the advancement of various coherent platforms. However, currently only a handful of feedback master equations exist in the literature, which are restricted to specific types of feedback. In this letter we first introduce a unifying framework, based on a single general equation, that describes all possible feedback schemes in sequentially (and continuously) measured systems, and from which all previous results follow. Next, we specialize it to the case of quantum jumps and introduce a new type of feedback based on the channel of the last detected jump, as well as the time elapsed since it occurred. Our description is experimentally grounded, and naturally allows for the introduction of realistic effects, such as time-delays in the feedback loop. We illustrate our results with two time-dependent feedback protocols conditioned on quantum-jump detections: one achieving population inversion of a two-level system against a thermal bath, and another enabling real-time reversal of quantum transitions, both admitting steady-state solutions.
Forward citations
Cited by 4 Pith papers
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An operational continuum limit of quantum combs
A continuous process tensor is defined by embedding the discrete multi-partite Choi matrix of a quantum comb into bosonic Fock space, closing the gap between discrete and continuum descriptions of multi-time quantum p...
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Deterministic Equations for Feedback Control of Open Quantum Systems III: Full counting statistics for jump-based feedback
Memory-based quantum-jump feedback is mapped to a Markovian Lindblad equation on an enlarged space, enabling full counting statistics of any counting observable.
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Deterministic Equations for Feedback Control of Open Quantum Systems II: Properties of the memory function
For feedback-driven monitored quantum systems, the memory function's statistics follow from a deterministic hybrid classical-quantum state; demonstrated on qubit cooling and Rabi stabilization.
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Deterministic quantum master equation for non-Markovian signal processing
A deterministic master equation for non-Markovian quantum feedback follows from rewriting finite-memory signal rules as higher-dimensional Markovian vector signals (Eq. 2), with momentum and T-step embeddings worked out.
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