  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.
