Quantum measurements can induce an entanglement transition between extensive and sub-extensive scaling of the entanglement entropy. This transition is of great interest since it illuminates the intricate physics of thermalization and control in open interacting quantum systems. Whilst this transition is well established for stroboscopic measurements in random quantum circuits, a crucial link to physical settings is its extension to continuous observations where, for an integrable model, it has been shown that a sub-extensive scaling appears for arbitrarily weak measurements.

 

In this talk, I present results for a one-dimensional quantum circuit evolving under random unitary transformations and generic positive operator-valued measurements of "variable strength". I will show that, for stroboscopic dynamics, there is a phase transition controlled by both the measurement density and the measurement strength. I will further show that the entanglement transition at a finite measurement strength persists for a continuously measured system with randomly non-integrable unitary evolution. I will finally present results for non-interacting models, in which a transition between logarithmic growth and strict localization of entanglement is still possible due to measurement induced dynamics. These results open the possibility to investigate the measurement induced entanglement transition in quantum architectures accessible via continuous measurements.