  In quantum mechanics, accidental degeneracy refers to energy degeneracy that
occurs coincidentally, without any protection by symmetry. Here, we prove a
theorem stating that any two-fold degeneracy (accidental or not) in a quantum
system is protected by a novel hidden symmetry, which can be expressed by an
antiunitary operator with its square being -1. In this sense, the so-called
accidental degeneracy is not really accidental, and this actually implies a
hidden antiunitary symmetry.
