  We propose an experiment for directly constructing and locally probing
topologically entangled states of superconducting vortices which can be
performed with present-day technology. Calculations using an elastic string
vortex model indicate that as the pitch (the winding angle divided by the
vertical distance) increases, the vortices approach each other. At values of
the pitch higher than a maximum value the entangled state becomes unstable to
collapse via a singularity of the model. We provide predicted experimental
signatures for both vortex entanglement and vortex cutting. The local probe we
propose can also be used to explore a wide range of other quantities.
