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

Abstract

We experimentally construct a novel three-qubit entangled W-superposition ($\mathrm{W}\bar{\mathrm{W}}$) state on an NMR quantum information processor. We give a measurement-based filtration protocol for the invertible local operation (ILO) that converts the $\mathrm{W}\bar{\mathrm{W}}$ 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 $\mathrm{W}\bar{\mathrm{W}}$ state using only two-party reduced density matrices. An intriguing fact unearthed recently is that the $\mathrm{W}\bar{\mathrm{W}}$ 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 $\mathrm{W}\bar{\mathrm{W}}$ state is interconvertible with the GHZ state, it stores entanglement very differently.