Perfect State Transfer of Mixed States and Purification in Central Spin Systems

TL;DR

This paper demonstrates a method for perfect state transfer and purification of mixed quantum states in central spin systems, with practical implementation in quantum dots, using a mapping to 1D chain transfer.

Contribution

It introduces a novel approach for swapping mixed states in central spin systems and provides an experimentally relevant implementation for nuclear spin quantum information exchange.

Findings

Achieves perfect state transfer in mixed states.

Enables nuclear spin purification.

Robust against decoherence and errors.

Abstract

We show how two many-body, generally mixed, quantum states can be swapped via collective, all-to-all interactions. Specifically, we present an experimentally relevant implementation for quantum dots that enables coherent exchange of quantum information between different species of nuclear spins, effectively achieving a perfect swap gate for qudits formed from these different species. This process also serves as a tool for nuclear spin purification. The results are obtained by mapping the problem onto perfect state transfer on a 1D chain. In the partially polarized limit, we demonstrate that the states can be exchanged independently of the initial state. We also assess the robustness of the procedure to decoherence and errors.