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Entropic Kullback‐Leibler type distance measures for quantum distributions
Author(s) -
Laguna Humberto G.,
Salazar Saúl J. C.,
Sagar Robin P.
Publication year - 2019
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.25984
Subject(s) - kullback–leibler divergence , harmonic oscillator , statistical physics , measure (data warehouse) , mutual information , quantum , mathematics , quantum mechanics , physics , statistics , computer science , data mining
Entropic distance measures for quantum mechanical probability distributions, which are characterized by nodal structure and symmetry holes, are considered. We illustrate how the Kullback‐Leibler (KL) distance is not well defined in some instances and propose instead the use of the cumulative residual Kullback‐Leibler (CRKL) distance. The KL and CRKL measures are compared and contrasted for some representative quantum mechanical systems: The particle in an infinite well, the harmonic oscillator, and hydrogenic systems. We present cases where CRKL can be used to obtain distances whereas KL cannot be used, and also highlight examples where the KL and CRKL measures yield different behaviors and interpretations. An extension of the CRKL definition is obtained for application to harmonic oscillator systems defined over [− ∞ , ∞ ]. Distance measures for two‐variable (particle) distributions are also considered to address generalizations of the mutual information correlation measure. The use of CRKL in measuring distances between orbitals is also discussed.