Many-body entanglement and topology from uncertainties and measurement-induced modes

We present universal characteristics of quantum entanglement and topology through virtual entanglement modes that fluctuate into existence in subsystem measurements. For generic interacting systems and extensive conserved quantities, these modes give rise to a statistical uncertainty which corresponds to entanglement entropies. Consequently, the measurement-induced modes provide directly observable route to entanglement and its scaling laws. Moreover, in topological systems, the measurement-induced edge modes give rise to quantized and nonanalytic uncertainties, providing easily accessible signatures of topology. Our work provides a much-needed direct method to probe the performance of emerging quantum simulators to realize entangled and topological states.