Separate measurement- and feedback-driven entanglement transitions in the stochastic control of chaos

TL;DR

This paper investigates measurement-induced entanglement and control phase transitions in a quantum system modeled after the Bernoulli map, revealing distinct universality classes for entanglement and control transitions under Clifford gate restrictions.

Contribution

It demonstrates the emergence of separate entanglement and control phase transitions with distinct universality classes in a quantum analog of the Bernoulli map under Clifford gate restrictions.

Findings

Entanglement and control transitions are separate with distinct universality classes.

Control transition exponents match those of the classical map (random walk).

Entanglement transition exponents resemble those in measurement-induced phase transitions.

Abstract

We study measurement-induced entanglement and control phase transitions in a quantum analog of the Bernoulli map subjected to a classically-inspired control protocol. When entangling gates are restricted to the Clifford group, separate entanglement ($p_\mathrm{ent}$) and control ($p_\mathrm{ctrl}$) transitions emerge, revealing two distinct universality classes. The control transition has critical exponents $\nu$ and $z$ consistent with the classical map (a random walk) while the entanglement transition is revealed to have similar exponents as the measurement-induced phase transition in Clifford hybrid dynamics. This is distinct from the case of generic entangling gates in the same model, where $p_\mathrm{ent} = p_\mathrm{ctrl}$ and universality is controlled by the random walk.