Observation of area laws in an interacting quantum field simulator

Information shared between parties quantifies their correlation. A fundamental observation that emerges from studies of information is the area law, which states that information shared between spatial subregions typically scales with the area of their boundary rather than their volume. In non-interacting, quantum many-body systems, where Gaussian statistics apply, the scaling of information measures is well understood and experimentally verified even for continuous quantum field simulators [1].  Within interacting systems, the readout of information measures is impeded by the complexity of state reconstruction. As such, no measurements beyond small quantum systems (e.g., composed of few particles) have been made.

 

In my talk I will present a data-driven, model agnostic approach, which allowed us experimentally demonstrate the area law of mutual information for strongly correlated quantum fields with tuneable interaction strength. Our results [2] detail the scaling of mutual information with subsystem volume, boundary area, and separation between spatial regions at finite temperature. Moreover, we quantify the total effect of non-Gaussian correlations using an information-theoretic measure --- relative entropy. Our presented approach is based just on the bitstrings provided by the measurement and therefore readily applicable to other platforms and observables, thus constituting a universal toolkit for probing information in interacting and strongly correlated quantum systems.  

 

Suported by the Leverhulme Research Leadership Award (RL2019-020), the the EU project SPINUS (Grant No. 101135699) and the ERC-AdG ``Emergence in Quantum Physics'' (EmQ) (Grant No. 101097858)

 

[1]  M. Tajik, et al. Nature Physics 19, 1022–1026 (2023) 10.1038/s41567-023-02027-1

[2]  M.T. Jarema,  et al. arXiv:2510.13783