Super Quantum Discord and Inferior "Geometric Discord" Based on Weak Measurement in Noninertial Frames

Maohuai Xiang, Jiliang Jing
2014 Journal of Quantum Information Science  
Instead of projective measurement, we use weak measurement to define quantum and geometric discords, and compare them with the normal quantum and geometric discords based on the projective measurement in noninertial frames. We find that using weak measurement to define quantum discord we can capture more quantum correlations compared with the projective measurement, so calling it super quantum discord. However, we note that the geometric discord based on the weak measurements becomes smaller,
more » ... we name it inferior "geometric discord". We also show that, although both the super quantum discord and the inferior "geometric discord" decrease with the increase of observer's acceleration, the super quantum discord/inferior "geometric discord" increases/decreases as the measurements become weak. These differences reveal that the definitions of the quantum and geometric discords are not too concordant with each other. 55 experimental precision, require us to consider such effects coming from relativity in practice, so this field has been attracted much attentions [3]-[7] recently. Entanglement, one of the most general quantum resource for quantum information tasks, has been studied fruitfully in noninertial frame [4]- [7] . However, as we all know, the entanglement has no advantage in some quantum information tasks, since certain quantum information processing tasks can still be done without it [8]- [10] . Another quantum resource called quantum discord [11]-[13], which represents the inaccessible information that cannot be extracted by measurements on one subsystem and is defined as the difference between the total and the classical correlation, is believed more practical and generalized than the entanglement. In this regard, Datta [14] calculated the quantum correlation between two relatively accelerated scalar modes, and showed that the quantum correlation that is measured by the quantum discord is greater and more robust than the entanglement. They claimed that the quantum discord, unlike the entanglement, still conserve a finite amount although in the limit of infinite acceleration. Wang et al. [15] studied the quantum discord and classical correlation sharing between modes of Dirac fields in the noninertial frame and discussed the relations between the quantum discord and the entanglement, and compared them with that for the Bosonic field. Besides, the geometric discord [16] [17] , which is considered to be the geometric version of the quantum discord and defined as (the square of) the Hilbert-Schmidt distance between the state in question and the nearest classical state, is also studied together with the relativistic effects [18] [19] . It should be pointed out that, although both the quantum and geometric discords can characterize the quantum correlations, some authors found that these two quantities are not too concordant with each other. M. Okrasa and Z. Walczak [20] pointed out that quantum discords do not give consistent results, namely quantum discord and the geometric discord do not necessarily imply the same ordering of two-qubit X -states, which means that
doi:10.4236/jqis.2014.41005 fatcat:3brbwmuzdzhzjfk52m74htjjdq