Currently, I'm learning about topological quantum computers.
In one of the explained techniques, cooper pairs in superconductors are considered, where a cooper pair with a hole form a Majorana bound state. The pair is at the zero energy level, and as non-zero energies are not allowed, this should protect the Majorana bound state. However, as we have a pair, it is possible for the particles to each have a non-zero and opposite energy. Effectively the total energy is still zero, but each of the particles has non-zero energy.
If we bring these particles far apart, there will be no interaction between them. Consequently, each of the two cannot move to a non-zero energy, as that would violate the particle-hole symmetry.
What I don't understand is: How can the particles be considered independent, such that their energy is protected and the particle remains at zero energy, while we still have the Majorana properties from the interaction of the two particles?