Quantum Inf Process (2016) 15:291–300
Geometric measure of quantum discord with weak
· Qing-Wen Wang
· Shu-Qian Shen
Received: 31 July 2015 / Accepted: 4 November 2015 / Published online: 18 November 2015
© Springer Science+Business Media New York 2015
Abstract Super quantum discord based on weak measurements was introduced by
Singh and Pati (Ann Phys 343:141–152, 2014). We propose a geometric way of quan-
tifying quantum discord with weak measurements. It is shown that this geometric
measure of quantum discord with weak measurements (GQDW) is linearly dependent
on geometric measure of quantum discord (Dakic et al. in Phys Rev Lett 105:190502,
2010) and only captures partial quantumness of the states. It is found that the quan-
tum correlation can be extracted by a sequence of inﬁnitesimal weak measurements.
Finally, the level surfaces of GQDW for Bell-diagonal states are depicted and the
results are demonstrated by explicit example.
Quantum discord (QD) introduced by Ollivier and Zurek  is fundamentally different
from entanglement  which plays a vital role in quantum information processing.
The QD, which can be nonzero even for some separable states, represents the locally
inaccessible information, which is the difference between total and classical corre-
College of Science, Shanghai University, Shanghai 200444, People’s Republic of China
College of Science, China University of Petroleum, Qingdao 266580, People’s Republic of China