Unbounded deterministic entanglement generation by autonomous quantum measurement and feedforward

Entanglement generation is crucial for the implementation of a plethora of quantum information processing tasks. Open quantum dynamics, including dissipation and measurements, provides a versatile approach to producing entanglement. However, standard open-system entangling schemes either require post-selection or conditional feedback, or focus on the stationary state regime, where the maximal amount of entanglement is ultimately set by parameters describing the dissipative process (i.e. the Liouvillian). Here, we propose a class of dissipative protocols, based on autonomous quantum measurement and feedforward, where the entanglement generation is deterministic, and can even grow indefinitely with evolution time in bosonic systems. While such entanglement exhibits a curious tradeoff with purity of the generated states, we also show how pure-state entanglement can be deterministically recovered via a single cycle of local measurement and feedback operations. Our results reveal a pathway for converting measurement-induced conditional entanglement into deterministic entanglement, and also shed new light on the entanglement generation mechanism via correlated dephasing. Furthermore, our feedforward-based approach opens up new possibilities of probing measurement-induced entanglement phase transitions in unconditional dynamics.