Comparing Geometric Discord and Negativity for Bipartite States

Abstract

The geometric discord $\mathcal{D}$ of a state is a measure of the quantumness of the state and the negativity $\mathcal{N}$ is a measure of the entanglement of a state. It was proved by D. Girolami and G. Adesso that for states on ${\mathbb{C}}^2\otimes {\mathbb{C}}^2$, the geometric discord is always greater than or equal to the square of the negativity and conjectured that this holds in general. S. Rana and P. Parashar showed that this relation does not hold for all states on ${\mathbb{C}}^2\otimes {\mathbb{C}}^n$ for $n>2$. We provide several analytic families of states on ${\mathbb{C}}^2\otimes {\mathbb{C}}^3$ violating this relation. Certain upper and lower bounds for ${\mathcal{N}}^2-\mathcal{D}$ are obtained for states on ${\mathbb{C}}^m\otimes {\mathbb{C}}^n$ for any $m,n\in \mathbb{N}$.

arXiv commentBounds for the difference of the square of the negativity and the geometric discord are improved. 9 pages, 4 figures

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Cited by in corpus (2)

• A comparative study of LQU and LQFI in general qubit-qutrit axially symmetric states
• Geometric quantum discord of an arbitrary two-qudit state: the exact value and general upper bounds