Wave-particle duality employing quantum coherence in superposition with non-orthogonal pointers

Understand

We propose the notion of quantum coherence for superpositions over states which are not necessarily mutually orthogonal.

• This anticipatedly leads to a resource theory of non-orthogonal coherence.
• We characterize free states and free operations in this theory, and connect the latter with free operations in the resource theory of quantum coherence for orthogonal bases.
• We show that the concept of non-orthogonal coherence naturally furnishes us with a wave-particle duality in quantum double-slit experiments where the channels beyond the slits are leaky between them.