Uncovering measurement-induced entanglement via directional adaptive dynamics and incomplete information

The rich entanglement dynamics and transitions exhibited by monitored quantum systems typically only exist in the conditional state, making observation extremely difficult. In this Letter, we construct a general recipe for mimicking the conditional entanglement dynamics of a monitored system in a corresponding measurement-free dissipative system involving directional interactions between the original system and a set of auxiliary register modes. This mirror setup autonomously implements a measurement-feedforward dynamics that effectively retains a coarse-grained measurement record. We illustrate our ideas in a bosonic system featuring a competition between entangling measurements and local unitary dynamics, and also discuss extensions to qubit systems and truly many-body systems.