DREAMS · Dynamics and REplica Analysis of Monitored Systems

The DREAMS (Dynamics and REplica Analysis of Monitored Systems) project aims to understand the physics of monitored quantum systems, i.e., many-body systems that periodically undergo a series of repeated local measurements. The competition between the monitoring and the unitary dynamics, which respectively favor and hinder the building up of non-local quantum correlations, can give rise to a measurement-induced phase transition. Such a transition can be detected, for example, by looking at the growth of the entanglement of a subsystem or the purification time-scale of an initially mixed state.As entanglement is a central quantity in quantum information, a complete understanding of the dynamics of monitored systems and their critical behavior would have significant consequences both at the theoretical level and in the development of quantum technologiessuch as error correction and quantum control via feedback. To this end, a replica approach has been recently proposed. This has the advantage of framing the evolution of the system in terms of linear equations, at the price of introducing the need for an analytic continuation of our results.DREAMS is divided into three parts. First, the dynamics of some fully-connected models will be investigated through the replica formalism. As the physics of these models is dominated by mean-field effects, it is possible to derive exact analytic solutions and understand the conditions under which critical behavior could emerge. Then, more realistic, finite-range interacting systems will be taken into account to probe the validity of our predictions in the presence of a spatial modulation of the coupling. An extensive numerical activity will be carried out to test our prediction. Finally, these results will be reinterpreted in light of the existing theoretical frameworks for monitored systems, trying to extract general predictions.