Effect of the readout efficiency of quantum measurement on the system entanglement

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 one-dimensional (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. Our results bear impact for a broad range of fields, ranging from quantum simulation platforms of random walks to questions related to measurement-induced phase transitions.