Quantum entanglement

Physics

Mathematics

Weak measurement

Quantum phase transition

Entropy (arrow of time)

Statistical physics

Ergodic theory

Phase transition

Phase space

Gaussian

Mathematical analysis

Political science

Quantum system

Quantum mechanics

Unitary state

Quantum

Physical review. B./Physical review. B

We show that weak measurements can induce a quantum phase transition of interacting many-body systems from an ergodic thermal phase with a large entropy to a nonergodic localized phase with a small entropy, but only if the measurement strength exceeds a critical value. We demonstrate this effect for a one-dimensional quantum circuit evolving under random unitary transformations and generic positive operator-valued measurements of variable strength. As opposed to projective measurements describing a restricted class of open systems, the measuring device is modeled as a continuous Gaussian probe, capturing a large class of environments. By employing data collapse and studying the enhanced fluctuations at the transition, we obtain a consistent phase boundary in the space of the measurement strength and the measurement probability, clearly demonstrating a critical value of the measurement strength below which the system is always ergodic, irrespective of the measurement probability. These findings provide guidance for quantum engineering of many-body systems by controlling their environment.

Entanglement transition from variable-strength weak measurements