Exact High-Temperature Quantum Area Law

Abstract:We prove a $\beta^{2}$ area law for the quantum mutual information of thermal states of local lattice Hamiltonians: for any bipartitioning $A|B$ and all inverse temperatures $\beta$ below a critical value $\beta^{*}$, we show $\mathcal{I}_{\beta}(A,B) \leqslant \tilde{f}(\beta)\, \beta^{2}\,|\partial_{AB}|$, where $|\partial_{AB}|$ denotes the size of the boundary region and $\tilde{f}(\beta)$ remains finite as $\beta \to 0$. This quadratic scaling improves the relationship between high-temperature correlations and macroscopic thermodynamics. While a linear area law implicitly permits a loose, temperature-independent upper bound on extractable work and binding energy, the quadratic scaling ensures that the nonequilibrium free energy available after decoupling regions and the total energy of the interface both are proportional to the area of the interface of $A|B$ and vanish as $\beta$ at high temperatures. These results show that the high-temperature mutual information and correlation are suppressed, respectively, quadratically and linearly in inverse temperature, which are consistent with the expected thermal decoupling in macroscopic thermodynamic quantities.

arXiv:2609.32329 [quant-ph]

(or arXiv:2609.32329v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.32329 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.