Waveparticle duality employing quantum coherence in superposition with nonorthogonal pointers
Abstract
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 nonorthogonal 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 nonorthogonal coherence naturally furnishes us with a waveparticle duality in quantum doubleslit experiments where the channels beyond the slits are leaky between them. Furthermore, we demonstrate existence of a unique maximally coherent qubit state corresponding to any given purity. In addition, and in contradistinction with the case of orthogonal bases, there appears a nontrivial minimally coherent qubit state for a given purity. We also study the behavior of quantum coherence for some typical configurations of nonorthogonal bases which have no analogs for orthogonal bases. We further investigate the problem of determining the energy cost of creating nonorthogonal coherence, and find that it scales linearly with the nonorthogonal coherence created.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 March 2020
 DOI:
 10.1088/17518121/ab741f
 arXiv:
 arXiv:1705.04343
 Bibcode:
 2020JPhA...53k5301D
 Keywords:

 quantum coherence;
 nonorthogonal pointers;
 waveparticle duality;
 incoherent operations;
 quantum doubleslit experiment;
 Quantum Physics
 EPrint:
 13 pages, 8 figures, close to the published version