Nonclassical correlations in subsystems of globally entangled quantum states

TL;DR

This paper investigates the relationship between global multipartite entanglement and nonclassical correlations in two-qubit subsystems, revealing that certain structured states show local discord indicative of global entanglement, with implications for quantum computation.

Contribution

It demonstrates that in structured quantum states, local discord correlates with global entanglement, and identifies exceptions like stabilizer states where nonclassical correlations are absent despite entanglement.

Findings

Weighted graph states show local discord indicates global entanglement.

Stabilizer states have entanglement but lack nonclassical correlations in subsystems.

No clear dependence between entanglement and discord in random 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.