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

TL;DR

This paper introduces a universal approach to characterize quantum entanglement and topology through measurement-induced modes, linking observable uncertainties to entanglement entropy and topological signatures in quantum systems.

Contribution

It proposes a novel method using virtual measurement-induced modes to directly observe entanglement and topological features in quantum systems, applicable to interacting and topological phases.

Findings

Measurement-induced modes relate to entanglement entropy.

Edge modes produce quantized uncertainties in topological systems.

Method enables direct probing of entanglement and topology in quantum simulators.

Abstract

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 non-analytic 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.