Finite-temperature persistence of the mutual-information scaling

Determine whether the inverse dependence of the minimum teleportation coupling on the excess mutual information between corresponding subregions of systems A and B persists at finite temperature.

Background

The paper studies an infinite-temperature three-party many-body teleportation protocol in which system A is divided into regions entangled with systems B and C. In this setting, the minimum coupling required for high-fidelity teleportation scales as g_min proportional to n divided by the distance Δ between the message-injection site and the region of A entangled with C.

The authors observe that, for the chosen subregions, the excess mutual information between corresponding subregions of A and B is exactly 2Δ bits. They therefore suggest that the coupling scaling may equivalently be interpreted as an inverse dependence on this excess mutual information. Whether this relation survives at finite temperature is left unresolved.

References

It would be worthwhile to test whether an analogous relation persists at finite temperature.

— Multi-Boundary Many-Body Quantum Teleportation  (2609.03053 - Schwartzman et al., 2 Sep 2026) in Section Conclusions, paragraph beginning “A further direction is to test the protocol at finite temperatures”