Non-Hermitian Dynamics for Noise-Cancelling Quantum Feedback

In the presence of continuous monitoring, the conditional evolution of a quantum system is stochastic. A stochastic master equation can express the relevant dynamics. In certain instances, unitary feedback can negate the stochasticity due to conditional evolution, leading to deterministic dynamics. Our work looks at constructive methods to find such feedback for general quantum systems. For pure states, we express the resultant noise-cancelled dynamics in terms of a non-Hermitian Hamiltonian. We unify noise-cancelling feedback across several known examples of entanglement stabilization tasks and compare the dynamics against spectral properties of the associated non-Hermitian Hamiltonian. Our work is relevant for designing feedback protocols for state preparation and stabilization of continuously monitored quantum systems.