The addition of non-unitary ingredients to many-body quantum dynamics has led to a series of exciting developments in recent years, including new out-of-equilibrium entanglement phases and phase transitions enabled by quantum measurements. I will present recent work  in which we show that a duality transformation between space and time on one hand, and unitarity and non-unitarity on the other, can be used to realize non-unitary evolutions whose steady states exhibit a rich variety of behavior in the scaling of their entanglement with subsystem size — from logarithmic to extensive to fractal. These fractally entangled states add a qualitatively new entry to the families of many-body quantum states that have been studied as energy eigenstates or dynamical steady states, whose entropy almost always displays either area-law, volume-law or logarithmic scaling. The range of steady-state entanglement scalings for the non-unitary evolution are closely related to the question of entanglement growth in time under different kinds of unitary dynamics, from localized to chaotic. This connection is sharpened by an exact mapping to unitary evolution with edge decoherence, in which information is irreversibly “radiated away” from one edge of the system. Finally, I will discuss how these ideas could be experimentally realized with present-day or near-term quantum technologies, and how spacetime duality allows us to mitigate (or eliminate altogether) the overhead from "postselection" of random measurement outcomes .
 Matteo Ippoliti, Tibor Rakovszky, Vedika Khemani, arxiv:2103.06873
 Matteo Ippoliti, Vedika Khemani, PRL 126, 060501 (2021)