  A spin-orbit coupled quantum wire, with one end proximate to an s-wave
superconductor, can become a topological superconductor, with a Majorana mode
localized at each end of the superconducting region. It was recently shown that
coupling one end of such a topological superconductor to $two$ normal channels
of interacting electrons leads to a novel type of frustration and a quantum
critical point when both channels couple with equal strength. We propose an
experimental method to access this critical point in a $single$ quantum wire
and show its resilience to disorder.
