  By coupling with a qubit, we demonstrate that qubit decoherence can
unambiguously detect the occurrence of ground-state degeneracy in many-body
systems. We first demonstrate universality using the two-band model.
Consequently, several exemplifications, focused on topological condensed matter
systems in one, two, and three dimensions, are presented to validate our
proposal. The key point is that qubit decoherence varies significantly when
energy bands touch each other at the Fermi surface. In addition, it can
partially reflect the degeneracy inside the band. This feature implies that
qubit decoherence can be used for reliable diagnosis of ground-state
degeneracy.
