Comparing Geometric Discord and Negativity for Bipartite States
| Autor: | Bag, Priyabrata, Dey, Santanu, Osaka, Hiroyuki |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Physics Letters A, Volume 383, Issue 33, 28 November 2019, 125973; https://doi.org/10.1016/j.physleta.2019.125973 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.physleta.2019.125973 |
| Popis: | 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 $m, n\in\mathbb{N}$. Comment: Bounds for the difference of the square of the negativity and the geometric discord are improved. 9 pages, 4 figures |
| Databáze: | arXiv |
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