Optimal local filtering operation for enhancing quantum entanglement

Quantum entanglement is an indispensable resource for many significant quantum information processing tasks. Thus, distilling more entanglement from less entangled resource is a task of practical significance and has been investigated for decades. Local filtering operation is a practical way to enhance quantum entanglement. In this research, we investigate the scenario of bipartite entanglement with general two-qubit resource to find the optimal strategy of filtering operations. We obtain the upper bound for the ratio of entanglement increase and find the corresponding optimal local filtering operation to achieve the maximal ratio. Our analysis shows that the upper bound ratio grows with the length of local Bloch vector, while the success probability decreases with it. Based on our result, we further investigate the performance of considering a general quantum measurement. Our result shows that local measurement cannot increase the expectation of quantum entanglement, which gives analytical evidence to the well-known fact that local operation cannot create quantum entanglement.