Witnessed entanglement and the geometric measure of quantum discord

Tiago Debarba, Thiago O. Maciel, Reinaldo O. Vianna

Published 2012-07-05, updated 2012-09-25Version 3

We establish relations between geometric quantum discord and entanglement quantifiers obtained by means of optimal witness operators. In particular, we prove a relation between negativity and geometric discord in the Hilbert-Schmidt norm, which is slightly different from a previous conjectured one [Phys. Rev. A 84, 052110 (2011)].We also show that, redefining the geometric discord with the trace norm, better bounds can be obtained. We illustrate our results numerically.