|
Résumé |
Continuously monitored quantum systems exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. Monitored systems with a conserved charge undergo a separate transition, inside the volume-law phase, between a “charge-sharp” phase in which measurements efficiently collapse charge fluctuations and a “charge-fuzzy” phase in which they do not. For one-dimensional systems, the charge sharpening transition between these phases is a Kosterlitz-Thouless transition. I will describe the statistical mechanics of this transition, and provide an interpretation of the charge-sharpening transition as a qualitative change in how much information an eavesdropper can learn about the global charge of the system from local charge measurements. This “learnability” interpretation suggests a scalable experimental method for studying the transition; I will present data applying this method on noisy quantum hardware, and discuss how the statistical mechanics model can be used for error mitigation. I will comment on generalizations to higher dimensions and general symmetries. |
