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

Abstract

We experimentally construct a three-qubit entangled W superposition (W¯¯¯¯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¯¯¯¯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¯¯¯¯W state using only two-party reduced density matrices. An intriguing fact unearthed recently is that the W¯¯¯¯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¯¯¯¯W state is interconvertible with the GHZ state, it stores entanglement very differently.