Role of Weak Measurements on States Ordering and Monogamy of Quantum Correlation

Abstract

The information-theoretic definition of quantum correlation, e.g., quantum discord, is measurement dependent. By considering the more general quantum measurements, weak measurements, which include the projective measurement as a limiting case, we show that while weak measurements can enable one to capture more quantumness of correlation in a state, it can also induce other counterintuitive quantum effects. Specifically, we show that the general measurements with different strengths can impose different orderings for quantum correlations of some states. It can also modify the monogamous character for certain classes of states as well which may diminish the usefulness of quantum correlation as a resource in some protocols. In this sense, we say that the weak measurements play a dual role in defining quantum correlation.

Weak quantum discord

“…Surprisingly, though, by introducing weak measurements in the original procedure for the derivation of the entropic quantum discord, Singh and Pati obtained what they called a super quantum discord [39], a quantifier that is greater than quantum discord. This fact was corroborated by a number of works via explicit calculations involving two-qubit states [40,41,42,43]. However, as pointed out by Xiang and Jing, who also noticed the discrepancy between the super quantum discord and the weak geometrical quantum discord in contexts involving non-inertial reference frames [44], there seems to be some inconsistency in all this.…”

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

“…Besides, B. Li et al [30] gave the necessary and sufficient condition for vanishing super discord. They also discussed the advantage of the weak measurement [31] and analysed the property of the weak measurement in quantum discord [32].…”

Quantum correlation cost of the weak measurement

“…It has been shown that super discord is not less than the quantum discord. Recently, the super quantum discord has attracted increasing interests [46][47][48][49][50]. In particular, it is surprising that the weak measurement can extract extra quantumness and the lost quantumness could even be resurrected by weak measurement [50].…”