Basis Dependence of Quantum Coherence for a Single Quantum State

Quantum coherence has emerged as a powerful way to quantify the degree of wave nature in a quantum system, with the complementary particle-like quantity being distinguishability. Quantum coherence can be determined using any orthonormal basis, which allows us to explore different facets of a quantum system’s wave nature. We find that a quantum system can have different degrees of quantum coherence when different bases are used. Each of these bases corresponds to a different physical aspect of the system. We explore this result by examining how the quantum coherences of a beam system in a Stern-Gerlach apparatus evolve with time. We find that coherences defined with respect to different bases for the same system can exhibit significantly different behaviors.