Natural atomic probabilities in quantum information theory

• Published in: Journal of computational and applied mathematics Vol. 233; no. 6; pp. 1483 - 1490
• Main Authors: Carrera, Edmundo M., Flores-Gallegos, Nelson, Esquivel, Rodolfo O.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Kidlington Elsevier B.V 15-01-2010; Elsevier
• Subjects: Ab initio calculations; Algebra; Atoms in molecules; Exact sciences and technology; Functional analysis; Global analysis, analysis on manifolds; Mathematical analysis; Mathematics; Number theory; Numerical analysis; Numerical analysis. Scientific computation; Quantum information theory; Relative entropy; Sciences and techniques of general use; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Atoms in molecules; Relative entropy; Quantum information theory; Ab initio calculations; Correlation; Large system; Entropy; Probability distribution; Numerical analysis; Applied mathematics; Quantum mechanics; Hilbert space; Quantum information; Cryptography; Quantum theory; Information theory
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2009.02.086

Quantum Information Theory has witnessed a great deal of interest in the recent years since its potential for allowing the possibility of quantum computation through quantum mechanics concepts such as entanglement, teleportation and cryptography. In Chemistry and Physics, von Neumann entropies may provide convenient measures for studying quantum and classical correlations in atoms and molecules. Besides, entropic measures in Hilbert space constitute a very useful tool in contrast with the ones in real space representation since they can be easily calculated for large systems. In this work, we show properties of natural atomic probabilities of a first reduced density matrix that are based on information theory principles which assure rotational invariance, positivity, and
N
- and
v-representability in the Atoms in Molecules (AIM) scheme. These (natural atomic orbital-based) probabilities allow the use of concepts such as relative, conditional, mutual, joint and non-common information entropies, to analyze physical and chemical phenomena between atoms or fragments in quantum systems with no additional computational cost. We provide with illustrative examples of the use of this type of atomic information probabilities in chemical process and systems.