Invariant Off-Diagonality: SICs as Equicoherent Quantum States

Abstract

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.

7 pages

References in corpus (3)

• Application of a resource theory for magic states to fault-tolerant quantum computing
• Discrete phase space and minimum-uncertainty states
• Geometric and Information-Theoretic Properties of the Hoggar Lines

Cited by in corpus (1)

• One-Shot Yield-Cost Relations in General Quantum Resource Theories