Observable estimation of entanglement of formation and quantum discord for bipartite mixed quantum states

We present observable lower and upper bounds for the entanglement of formation (EOF) and quantum discord (QD), which facilitates estimates of EOF and QD for arbitrary experimental unknown states in finite-dimensional bipartite systems. These bounds can be easily obtained by a few experimental measurements on a twofold copy $\varrho \otimes \varrho$ of the mixed states. Based on our results, we use the experimental measurement data of the real experiment given by Schmid $\mathit{\text{et}}\mathit{\text{al.}}$ [Phys. Rev. Lett. $\mathbf{\text{101}}$, 260505 (2008)] to obtain the lower and upper bounds of EOF and QD for the experimental unknown state.