Entanglement-preserving limit cycles from sequential quantum measurements and feedback
Philippe Lewalle, Cyril Elouard, Andrew N. Jordan
Abstract
Entanglement generation and preservation is a key task in quantum information processing, and a variety of protocols exist to entangle remote qubits via measurement of their spontaneous emission. We here propose feedback methods, based on monitoring the fluorescence of two qubits and using only local $\ensuremath{\pi}$ pulses for control, to increase the yield and/or lifetime of entangled two-qubit states. Specifically, we describe a protocol based on photodetection of spontaneous emission (i.e., using quantum jump trajectories) which allows for entanglement preservation via measurement undoing, creating a limit cycle around Bell states. We then demonstrate that a similar modification can be made to a recent feedback scheme based on homodyne measurement (i.e., using diffusive quantum trajectories) [L. S. Martin and K. B. Whaley, arXiv:1912.00067] in order to increase the lifetime of the entanglement it creates. Our schemes are most effective for high measurement efficiencies, and the impact of less-than-ideal measurement efficiency is quantified. Our method provides a pathway towards generating and protecting entangled states, complementing others in the literature with similar aims, such that two-qubit entanglement may be used in various applications on demand.