Nonclassical correlations in subsystems of globally entangled quantum states

Abstract: The relation between genuine multipartite entanglement in the pure state of a collection of N qubits and the nonclassical correlations in its two-qubit subsystems is studied. Quantum discord is used as the quantifier of nonclassical correlations in the subsystem while the generalised geometric measure (GGM) [Phys. Rev. A. 81, 012308 (2010)] is used to quantify global entanglement in the N-qubit state. While no definite discernible dependence between the two can be found for randomly generated global states, for those with additional structure like weighted graph states we find that local discord is indicative of global multipartite entanglement. Global states that admit efficient classical descriptions like stabilizer states furnish an exception in which despite multipartite entanglement, nonclassical correlation is absent in two qubit subsystems. We discuss these results in the context of mixed state quantum computation where nonclassical correlation is considered a candidate resource that enables exponential speedup over classical computers.