Quantum entanglement estimation via symmetric-measurement-based positive maps

We provide a class of positive and trace-preserving maps based on symmetric measurements. From these positive maps we present separability criteria, entanglement witnesses, and the lower bounds of concurrence. We show by detailed examples that our separability criteria, entanglement witnesses, and lower bounds can detect and estimate the quantum entanglement better than existing related results.

Figure 1

Lower bounds with respect to the parameters $z$ and $q_1$.

Figure 2

Lower bound given in (31) (solid line) and in (32) (dashed line) as a function of $q_1$.