  Monitored quantum systems evolve along stochastic trajectories correlated
with the observer's knowledge of the system's state. Under such dynamics,
certain quantum resources like entanglement may depend on the observer's state
of knowledge. Here, we quantify the entanglement for a particle on a 1d quantum
random walk under inefficient monitoring using a mixed state-entanglement
measure -- the configuration coherence. We find that the system's maximal mean
entanglement at the measurement-induced quantum-to-classical crossover is
suppressed in different ways by the measurement strength and inefficiency. In
principle, strong measurements can lower the amount of entanglement
indefinitely. However, at a given measurement strength, efficient readout can
crucially increase the system entanglement, making high-fidelity detectors
essential for successful quantum computing.
