Local entanglement of multidimensional continuous-variable systems

We study the `local entanglement' remaining after filtering operations corresponding to imperfect measurements performed by one or both parties, such that the parties can only determine whether or not the system is located in some region of space. The local entanglement in pure states of general bipartite multidimensional continuous-variable systems can be completely determined through simple expressions. We apply our approach to semiclassical WKB systems, multi-dimensional harmonic oscillators, and a hydrogen atom as three examples.