Area laws from classical entropies

TL;DR

This paper demonstrates that classical entropies derived from measurement distributions exhibit area law scaling similar to quantum entropies, enabling new ways to analyze quantum phenomena through classical observables.

Contribution

It shows that classical entropies can display area law behavior, linking quantum entanglement features to classical measurement data, broadening analysis methods.

Findings

Classical entropies follow area law scaling in various quantum states.

Quantities like central charge and temperature are encoded in classical observables.

Classical entropies can replace quantum entropies in probing quantum phenomena.

Abstract

The area law-like scaling of local quantum entropies is the central characteristic of the entanglement inherent in quantum fields, many-body systems, and spacetime. Whilst the area law is primarily associated with the entanglement structure of the underlying quantum state, we here show that it equally manifests in classical entropies over measurement distributions when vacuum contributions dictated by the uncertainty principle are subtracted. Using the examples of the Gaussian ground and thermal states, but also the non-Gaussian particle state of a relativistic scalar field, we present analytical and numerical area laws for the entropies of various distributions and unveil how quantities of widespread interest such as the central charge and the (local) temperature are encoded in classical observables. With our approach, quantum entropies are no longer necessary to probe quantum phenomena, thereby rendering area laws and other quantum features directly accessible to theoretical models of high complexity as well as state-of-the-art experiments.