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npj Quantum Information

Superfluid helium thin films as quantum field theory simulators for probing information area laws

Maciej T. Jarema, Cameron R. D. Bunney, Vitor S. Barroso, Mohammadamin Tajik, Chris Goodwin, Silke Weinfurtner

Published Sep 15, 2026• 0 citations
Publisher

Abstract

Abstract Information-theoretic measures, such as entropy and mutual information, provide a comprehensive tool for characterising quantum correlations. They reveal foundational features across quantum many-body systems, quantum field theory (QFT), and even black hole thermodynamics. A striking example is the emergence of area laws , occurring when correlations are constrained to local regions, causing information to scale with boundary area, rather than volume. Whilst area laws have been experimentally observed in discrete quantum systems, they remain under-explored in continuous quantum fields owing to the lack of implementable measurement techniques in these settings. Here, we propose using phononic excitations (third sound) on thin-film superfluid helium as a (2 + 1)-dimensional quantum field simulator. In light of recent advances in high-resolution detection schemes, this platform now offers experimental access to the spatially and temporally resolved effective field. We develop a framework to utilise experimentally accessible observables to reconstruct the covariance matrix and evaluate distributions of mutual information. Our numerical predictions confirm area-law behaviour with characteristic deviations due to effects of confinement. Finally, we outline a clear pathway towards experimental implementation of our proposal considering state-of-the-art imaging and cryogenic technologies.

DOI
10.1038/s41534-026-01367-z

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Abstract Information-theoretic measures, such as entropy and mutual information, provide a comprehensive tool for characterising quantum correlations. They reveal foundational features across quantum many-body systems, quantum field theory (QFT), and even black hole thermodynamics. A striking example is the emergence of area laws , occurring when correlations are constrained to local regions, causing information to scale with boundary area, rather than volume. Whilst area laws have been experimentally observed in discrete quantum systems, they remain under-explored in continuous quantum fields owing to the lack of implementable measurement techniques in these settings. Here, we propose using phononic excitations (third sound) on thin-film superfluid helium as a (2 + 1)-dimensional quantum field simulator. In light of recent advances in high-resolution detection schemes, this platform now offers experimental access to the spatially and temporally resolved effective field. We develop a framework to utilise experimentally accessible observables to reconstruct the covariance matrix and evaluate distributions of mutual information. Our numerical predictions confirm area-law behaviour with characteristic deviations due to effects of confinement. Finally, we outline a clear pathway towards experimental implementation of our proposal considering state-of-the-art imaging and cryogenic technologies.
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)(2 + 1)(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.
Information shared between parties quantifies their correlation. The encoding of correlations across space and time characterises the structure, history, and interactions of systems. One of the most fundamental properties 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. 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, localised particles) have been made. Here, we fill this gap by experimentally demonstrating the area law of mutual information in an ultra-cold atom simulator of quantum fields with tuneable interaction strength. Our results 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 data-driven, model agnostic, and readily applicable to other platforms and observables, thus constituting a universal toolkit for probing information in high-dimensional quantum systems and its role in shaping quantum matter and spacetime.
Theoretical understanding of the scaling of entropies and the mutual information has led to significant advances in the research of correlated states of matter, quantum field theory, and gravity. Measuring von Neumann entropy in quantum many-body systems is challenging as it requires complete knowledge of the density matrix. In this work, we measure the von Neumann entropy of spatially extended subsystems in an ultra-cold atom simulator of one-dimensional quantum field theories. We experimentally verify one of the fundamental properties of equilibrium states of gapped quantum many-body systems, the area law of quantum mutual information. We also study the dependence of mutual information on temperature and the separation between the subsystems. Our work is a crucial step toward employing ultra-cold atom simulators to probe entanglement in quantum field theories.
Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: the entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such ``area laws'' for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum many-body physics where they have important implications on the numerical simulation of lattice models. In this Colloquium the current status of area laws in these fields is reviewed. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation in quantum lattice models, and disordered systems, nonequilibrium situations, and topological entanglement entropies are discussed. These questions are considered in classical and quantum systems, in their ground and thermal states, for a variety of correlation measures. A significant proportion is devoted to the clear and quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. Matrix-product states, higher-dimensional analogs, and variational sets from entanglement renormalization are also discussed and the paper is concluded by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations of quantum states.
The scaling of local quantum entropies is of utmost interest for characterizing quantum fields, many-body systems, and gravity. Despite their importance, theoretically and experimentally accessing quantum entropies is challenging as they are nonlinear functionals of the underlying quantum state. Here, we show that suitably chosen classical entropies capture many features of their quantum analogs for an experimentally relevant setting. We describe the post-quench dynamics of a multi-well spin-1 Bose-Einstein condensate from an initial product state via measurement distributions of spin observables and estimate the corresponding entropies using the asymptotically unbiased kkk-nearest neighbor method. We observe the dynamical build-up of quantum correlations signaled by an area law, as well as local thermalization revealed by a transition to a volume law, both in regimes characterized by non-Gaussian distributions. We emphasize that all relevant features can be observed at small sample numbers without reconstructing the underlying state or measurement distributions, rendering our method directly applicable to a large variety of models and experimental platforms.
Entanglement entropy is a fundamental concept with rising importance in various fields ranging from quantum information science, black holes to materials science. In complex materials and systems, entanglement entropy provides insight into the collective degrees of freedom that underlie the systems' complex behaviours. As well-known predictions, the entanglement entropy exhibits area laws for systems with gapped excitations, whereas it follows the Gioev-Klich-Widom scaling law in gapless fermion systems. However, many of these fundamental predictions have not yet been confirmed in experiments due to the difficulties in measuring entanglement entropy in physical systems. Here, we report the experimental verification of the above predictions by probing the nonlocal correlations in phononic systems. We obtain the entanglement entropy and entanglement spectrum for phononic systems with the fermion filling analog. With these measurements, we verify the Gioev-Klich-Widom scaling law. We further observe the salient signatures of topological phases in entanglement entropy and entanglement spectrum.