Quantum coherence via skew information and its polygamy

Quantifying coherence is a key task in both quantum-mechanical theory and practical applications. Here, a reliable quantum coherence measure is presented by utilizing the quantum skew information of the state of interest subject to a certain broken observable. This coherence measure is proven to fulfill all the criteria (especially the strong monotonicity) recently introduced in the resource theories of quantum coherence. The coherence measure has an analytic expression and an obvious operational meaning related to quantum metrology. In terms of this coherence measure, the distribution of the quantum coherence, i.e., how the quantum coherence is distributed among the multiple parties, is studied and a corresponding polygamy relation is proposed. As a further application, it is found that the coherence measure forms the natural upper bounds for quantum correlations prepared by incoherent operations. The experimental measurements of our coherence measure as well as the relative-entropy coherence and $l_p$-norm coherence are studied finally.

Figure 1

All the density matrices ${\rho }_{AB}$ are generated in $(2\otimes 3)$-dimensional Hilbert space.

Figure 2

All the density matrices ${\rho }_{AB}$ are generated in $(3\otimes 3)$-dimensional Hilbert space.

Figure 3

All the density matrices ${\rho }_{AB}$ are generated in $(3\otimes 4)$-dimensional Hilbert space.

Figure 4

All the density matrices ${\rho }_{AB}$ are generated in $(4\otimes 4)$-dimensional Hilbert space.