Experimental construction of a W-superposition state and its equivalence to the GHZ state under local filtration

TL;DR

This paper experimentally constructs a novel three-qubit W-superposition state on an NMR platform, demonstrating its equivalence to the GHZ state under local operations and its unique reconstructibility from two-party reduced states.

Contribution

It introduces the experimental creation of the W-superposition state and shows its equivalence to GHZ under local filtration, along with a protocol for reconstructing it from reduced states.

Findings

W-superposition state successfully constructed on NMR platform

W-superposition state is equivalent to GHZ under local filtration

W-superposition state can be reconstructed from two-party reduced density matrices

Abstract

We experimentally construct a novel three-qubit entangled W-superposition ($\rm W \bar{\rm W}$) state on an NMR quantum information processor. We give a measurement-based filtration protocol for the invertible local operation (ILO) that converts the $\rm W \bar{\rm W}$ state to the GHZ state, using a register of three ancilla qubits. Further we implement an experimental protocol to reconstruct full information about the three-party $\rm W \bar{\rm W}$ state using only two-party reduced density matrices. An intriguing fact unearthed recently is that the $\rm W \bar{\rm W}$ state which is equivalent to the GHZ state under ILO, is in fact reconstructible from its two-party reduced density matrices, unlike the GHZ state. We hence demonstrate that although the $\rm W \bar{\rm W}$ state is interconvertible with the GHZ state, it stores entanglement very differently.