Equivalence regimes for geometric quantum discord and local quantum uncertainty

TL;DR

This paper demonstrates the equivalence of geometric quantum discord and local quantum uncertainty in bipartite systems and shows their effectiveness in quantifying quantum correlations affecting phase estimation.

Contribution

It establishes the equivalence between two measures of quantum discord for bipartite systems and highlights their practical relevance in quantum metrology.

Findings

The two measures are equivalent for 2 x D systems.

Both measures quantify the decrease in quantum Fisher information.

They are computationally accessible for certain quantum systems.

Abstract

The concept of quantum discord aims at unveiling quantum correlations that go beyond those described by entanglement. Its original formulation [J. Phys. A 34, 6899 (2001); Phys. Rev. Lett 88, 017901 (2002)] is difficult to compute even for the simplest case of two-qubits systems. Alternative formulations have been developed to address this drawback, such as the geometric measure of quantum discord [Phys. Rev. A 87, 062303 (2013)] and the local quantum uncertainty [Phys. Rev. Lett 110, 240402 (2013)] that can be evaluated in closed form for some quantum systems, such as two-qubit systems. We show here that these two measures of quantum discord are equivalent for 2 x D dimensional bipartite quantum systems. By considering the relevant example of N00N states for phase estimation in lossy environments, we also show that both metrics of quantum discord quantify the decrease of quantum Fisher information of the phase estimation protocol. Given their ease of computation in 2 x D bipartite systems, the geometric measure of quantum discord and the local quantum uncertainty demonstrate their relevance as computable measures of quantum discord.