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

摘要

We experimentally construct a novel three-qubit entangled W-superposition($\rm W \bar{\rm W}$) state on an NMR quantum information processor. We give ameasurement-based filtration protocol for the invertible local operation (ILO)that converts the $\rm W \bar{\rm W}$ state to the GHZ state, using a registerof three ancilla qubits. Further we implement an experimental protocol toreconstruct full information about the three-party $\rm W \bar{\rm W}$ stateusing only two-party reduced density matrices. An intriguing fact unearthedrecently is that the $\rm W \bar{\rm W}$ state which is equivalent to the GHZstate under ILO, is in fact reconstructible from its two-party reduced densitymatrices, unlike the GHZ state. We hence demonstrate that although the $\rm W\bar{\rm W}$ state is interconvertible with the GHZ state, it storesentanglement very differently.