Experimental construction of aWsuperposition state and its equivalence to the Greenberger-Horne-Zeilinger state under local filtration

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