Experimental construction of a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>W</mml:mi></mml:math>superposition state and its equivalence to the Greenberger-Horne-Zeilinger state under local filtration

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