Equivalence regimes for geometric quantum discord and local quantum uncertainty

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 × 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 × D bipartite systems, the geometric measure of quantum discord and the local quantum uncertainty demonstrate their relevance as computable measures of quantum discord.

A note on hidden quantum discord in two- and three-qubit systems under local filtering operations

“…In addition to the research on the definition and the calculation of quantum discord, discord in other directions has recently been considered: Luo et al elaborated on the relationship between quantum coherence and quantum uncertainty, and proposed that quantum discord is actually the minimized quantum coherence [13]. Oscar et al have proved that for a 2 × D-dimensional system, geometric quantum discord and local quantum uncertainty are equivalent while arbitrary dimensions are not [14].…”