The concept of quantum discord aims at unveiling quantum correlations that go beyond those described by entanglement. Its original formulation [L. Henderson and V. Vedral, J. Phys. A: Math. Gen. 34, 6899 (2001); H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2001)] 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 [L. Chang and S. Luo, Phys. Rev. A 87, 062303 (2013)] and the local quantum uncertainty [D. Girolami, T. Tufarelli, and G. Adesso, 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.We acknowledge support from the Spanish Ministry of
Economy and Competitiveness (“Severo Ochoa” program
for Centres of Excellence in R&D No. SEV-2015-0522),
from Fundacio Privada Cellex, from Fundacio Mir-Puig, and
from Generalitat de Catalunya through the CERCA program.
This work was partially funded through the EMPIR
project 17FUN01-BeCOMe. The EMPIR initiative is cofunded
by the European Union Horizon 2020 Research and
Innovation Programme and the EMPIR participating states.
A.V. acknowledges financial support from PREBIST that
has received funding from the European Union Horizon
2020 Research and Innovation Programme under the Marie
Sklodowska-Curie Grant Agreement No. 754558. J.R.A. acknowledges
funding by the European Union Horizon 2020
Research and Innovation Programme (Marie Sklodowska-
Curie 765075-LIMQUET). R.J.L.M. thankfully acknowledges
financial support by CONACyT under the project
CB-2016-01/284372, and by Direcci n General de Asuntos
del Personal Acad mico, Universidad Nacional Aut noma de
M xico (DGAPA-UNAM), under the project UNAM-PAPIIT
IN102920.Peer ReviewedPostprint (author's final draft
