Heisenberg chains cannot mirror a state

TL;DR

This paper demonstrates that Heisenberg spin chains without local magnetic fields cannot naturally mirror quantum states, challenging their use for quantum information transfer.

Contribution

It proves that Heisenberg chains without local magnetic fields inherently lack the ability to perform natural state mirroring, clarifying limitations for quantum communication.

Findings

Heisenberg chains without local magnetic fields cannot mirror states.

State mirroring is not a natural feature of these chains.

Implications for quantum communication protocols.

Abstract

Faithful exchange of quantum information can in future become a key part of many computational algorithms. Some Authors suggest to use chains of mutually coupled spins as channels for quantum communication. One can divide these proposals into the groups of assisted protocols, which require some additional action from the users, and natural ones, based on the concept of state mirroring. We show that mirror is fundamentally not the feature chains of spins-1/2 coupled by the Heisenberg interaction, but without local magnetic fields. This fact has certain consequences in terms of the natural state transfer.