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Super quantum correlation and geometry for Bell-diagonal states with weak measurements
Yao-Kun Wang, Teng Ma, Heng Fan, Shao-Ming Fei and Zhi-Xi Wang
We propose "super one-way deficit" by weak measurement as the generalization of one-way deficit defined for standard projective measurement. The super one-way deficit for Werner state is obtained analytically. We find that super one-way deficit is smaller than the standard one-way deficit, which is contrary to a straightforward expectation based on the known fact that super quantum discord by weak measurement is always larger than the quantum discord defined by projective measurement. On the other hand, by tuning the weak measurement continuously to the projective measurement, both super one-way deficit and super quantum discord converge to the same value, which is either the one-way deficit or the quantum discord both quantifying quantum correlation. In this sense, weak measurement does not necessarily capture more quantumness of correlations. We also give the geometry of super quantum discord of the Bell-diagonal states with explicit geometrical figures. As an application, the dynamic behavior of super quantum correlation including super quantum discord and super one-way deficit under decoherence is investigated. We find that the order relation of the super quantum correlation and the quantum correlation keep unchanged under the phase flipping channel for the Bell-diagonal states and the Werner states. Super quantum discord with weak measurements as introduced by Uttam Singh and Arun Kumar Pati is always larger than the quantum discord captured by the strong measurements, and weak measurements reveal more quantumnessis. But the latter is not true. We will give another super quantum correlation, called as "super one-way deficit", and analytically evaluate super one-way deficit of the Werner states is always smaller than the one-way deficit, in other words, weak measurements do not always capture more quantum correlation. We also give the geometry of super quantum discord of the Bell-diagonal states. As an application, the dynamic behavior of super quantum correlation including super quantum discord and super one-way deficit under decoherence is investigated.