Invariant Off-Diagonality: SICs as Equicoherent Quantum States

Understand

Coherence, treated as a resource in quantum information theory, is a basis-dependent quantity.

• Looking for states that have constant coherence under canonical changes of basis yields highly symmetric structures in state space.
• For the case of a qubit, we find an easy construction of qubit SICs (Symmetric Informationally Complete POVMs).
• SICs in dimension 3 and 8 are also shown to be equicoherent.