  We demonstrate that entangled electron-hole pairs can be produced and
detected in a quantum spin Hall insulator with a constriction that allows for a
weak inter-edge tunneling. A violation of a Bell inequality, which can be
constructed in terms of low-frequency nonlocal current-current correlations,
serves as a detection of the entanglement. We show that the maximum violation
of a Bell inequality can be naturally achieved in this setup, without a need to
fine tune tunneling parameters. This may provide a viable route to producing
spin entanglement in the absence of any correlations and pairing, where
spin-to-charge conversion is enabled by the helical edge structure of a quantum
spin Hall insulator.
