## Necessary and sufficient conditions for local creation of quantum discord    [PDF]

Yu Guo, Jinchuan Hou
In this paper, we confirm the conjecture proposed in [X. Hu \emph{et al}., Phys. Rev. A \textbf{85}, 032102(2012)]: A local channel can't create quantum discord (QD) for zero QD states if and only if it is either a completely decohering channel or an isotropic channel for any qudit systems with $d\geq3$. In addition, the explicit form of local channel that can't create QD for zero QD states is presented for the qubit system, which improves the result in [A. Streltsov \emph{et al}., Phys. Rev. Lett. \textbf{107}, 190502(2011)]. Moreover, we show that i) a qudit ($d\geq3$) local channel preserves zero QD states in both directions (namely, the output state under the channel has zero QD if and only if the input state has zero QD) if and only if it is a nontrivial isotropic channel, ii) there exist non isotropic local channels that preserve zero QD states in both directions for the qubit system, and iii) a local channel nullifies QD in any state if and only if it is a completely decohering channel. In particular, the explicit form of decohering channel is investigated.
View original: http://arxiv.org/abs/1206.2159