Precision of the analogy between three-sided teleportation and finite-temperature holographic teleportation

Establish whether the intermediate-time fidelity peak in the three-party zero-dimensional teleportation protocol can be quantitatively related to the peak near the scrambling time in finite-temperature two-sided holographic teleportation.

Background

The paper identifies a qualitative similarity between the intermediate-time fidelity peak observed when the message is initially inserted in a region entangled with the third party and the fidelity peak near the scrambling time in finite-temperature two-sided holographic teleportation.

The authors propose a tensor-network and quasiparticle-inspired interpretation of this similarity but explicitly state that making the comparison precise requires further work. The unresolved issue is whether the analogy can be formulated quantitatively rather than remaining purely phenomenological.