IAS CMP/QFT Group Meeting

Abstract: How well can an observer making local measurements learn about global properties of a system, e.g., its charge? I will motivate this question in the quantum setting, and then turn to some results on classical stochastic processes. I will discuss two phase transitions in inference, which are conceptually closely related. First [1], when the stochastic evolution is interrupted by continuous measurements, there is a phase transition as a function of measurement rate between a "learnable" phase at high measurement rate where measurements rapidly fix the charge profile and an "unlearnable" phase where they do not. Second [2], after stochastic evolution for a time greater than some threshold t*, the charge fluctuations undergo a phase transition in local retrievability: beyond the threshold, if one loses access to a region of the system, retrieving the charge in the lost region requires nonlocal information about the rest of the system. I will discuss the critical properties of both of these "learnability" transitions. 

[1] F. Barratt et al., PRL 129, 200602 (2022); SG et al., PRX 16, 011024 (2026).

[2] J. Hauser et al., arxiv:2602.16045