  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.
