Experimental construction of generic three-qubit states and their reconstruction from two-party reduced states on an NMR quantum information processor

TL;DR

This paper experimentally constructs a canonical form for three-qubit states on an NMR processor, demonstrating state preparation, special cases, and state reconstruction from two-qubit reduced states with high fidelity.

Contribution

It introduces a practical scheme to realize a canonical form for three-qubit states, including GHZ and W states, and demonstrates their reconstruction from two-qubit reduced states.

Findings

Successful experimental realization of a generic three-qubit state on NMR

High-fidelity state preparation confirmed by tomography

Reconstruction of three-qubit states from two-qubit reduced states for most pure states

Abstract

We experimentally explore the state space of three qubits on an NMR quantum information processor. We construct a scheme to experimentally realize a canonical form for general three-qubit states up to single-qubit unitaries. This form involves a non-trivial combination of GHZ and W-type maximally entangled states of three qubits. The general circuit that we have constructed for the generic state reduces to those for GHZ and W states as special cases. The experimental construction of a generic state is carried out for a nontrivial set of parameters and the good fidelity of preparation is confirmed by complete state tomography. The GHZ and W-states are constructed as special cases of the general experimental scheme. Further, we experimentally demonstrate a curious fact about three-qubit states, where for almost all pure states, the two-qubit reduced states can be used to reconstruct the full three-qubit state. For the case of a generic state and for the W-state, we demonstrate this method of reconstruction by comparing it with the directly tomographed three-qubit state.