Information in quantum field theory simulators: Thin-film superfluid helium

TL;DR

This paper proposes a method to measure quantum mutual information in a superfluid helium thin film simulator, demonstrating area-law scaling and finite-size effects through numerical predictions, advancing experimental quantum field theory studies.

Contribution

It introduces an experimental approach to measure quantum correlations in continuous systems using superfluid helium thin films, bridging theory and experiment.

Findings

Numerical predictions show area-law scaling of mutual information.

Finite system size causes deviations from ideal area-law behavior.

Methodology enables experimental exploration of quantum correlations in continuous systems.

Abstract

Understanding quantum correlations through information-theoretic measures is fundamental to developments in quantum field theory, quantum information, and quantum many-body physics. A central feature in a plethora of systems is the area law, under which information scales with the size of the boundary of the system, rather than volume. Whilst many systems and regimes exhibiting an area law have been identified theoretically, experimental verification remains limited, particularly in continuous systems. We present a methodology for measuring mutual information in an experimental simulator of non-interacting quantum fields, and propose using the analogue $(2 + 1)$-dimensional spacetime offered by thin films of superfluid helium. We provide numerical predictions incorporating the natural thermal state of the helium sample that exemplify an area-law scaling of mutual information, and characterise deviations attributable to the inherent finite system size.