Universal Features of Critical Mixed States Obtained from Measurement and Feedback

Recent advances in quantum simulators enable the engineering of long-range

entangled mixed states using mid-circuit measurements and feedback protocols. In this

work, we explore the universal features of critical mixed states obtained from a single

round of measurement followed by feedback. We characterize the universality classes

of these mixed states with defect entropy and scaling of entanglement negativity, a

measure of mixed-state quantum entanglement. Through a combination of field theory

and numerical simulations, we discover that these mixed states exhibit a universal

subleading term in their entropies, governed by the "g-function." This g-function allows

us to associate the critical mixed states with renormalization group fixed points.

Specifically, we discover an example of critical mixed state with non-trivial g-function

and logarithmic negativity scaling. For a family of critical mixed states obtained from

interacting spinful fermions, we analytically compute their g-functions and find a

continuous dependency on the Luttinger parameters.