  A quantum-enhanced experiment, in which information is transduced from a
system of interest and processed on a quantum computer, has the possibility of
exponential advantage in sampling tasks over a traditional experiment, where
only the measurement outcomes of projective or weak measurements are stored on
a classical computer. In this work, we demonstrate that, similar to the
measurement induced phase transition~(MIPT) occurring in traditional
experiments, quantum-enhanced experiments can also show entanglement phase
transitions. We introduce a noisy transduction operation which replaces
projective measurements and acts independently on two qubits, recording the
quantum state of one qubit in the measurement apparatus, while erasing the
quantum state of the other qubit with the environment. We then construct a
random brickwork circuit which shows an entanglement transition tuned by the
rate of noisy transduction operations. Below the critical rate of noisy
transduction, an extensive amount of entanglement is generated between regions
of the system and apparatus, while above the critical rate, entanglement
satisfies area law scaling. Our work delineates the prerequisites for
quantum-enhanced experiments to manifest entanglement transitions, thereby
establishing a foundational framework that connects quantum-enhanced sensing
with emergent entanglement phenomena.
