Transforming pure and mixed states using an NMR quantum homogeniser

TL;DR

This paper demonstrates an NMR-based implementation of a quantum homogeniser that can transform qubit states with high accuracy, exploring symmetry in pure and mixed state homogenisation and its implications for state preparation and information scrambling.

Contribution

First experimental realization of a finite quantum homogeniser using NMR with four qubits, analyzing symmetry in state transformations and implications for quantum information.

Findings

Experimental results align with theoretical symmetry predictions

Homogeniser effectively transforms pure and mixed states

Decoherence effects are accounted for in analysis

Abstract

The universal quantum homogeniser can transform a qubit from any state to any other state with arbitrary accuracy, using only unitary transformations to perform this task. Here we present an implementation of a finite quantum homogeniser using nuclear magnetic resonance (NMR), with a four-qubit system. We compare the homogenisation of a mixed state to a pure state, and the reverse process. After accounting for the effects of decoherence in the system, we find the experimental results to be consistent with the theoretical symmetry in how the qubit states evolve in the two cases. We analyse the implications of this symmetry by interpreting the homogeniser as a physical implementation of pure state preparation and information scrambling.