Information and quantum theories: an analysis in one-dimensional systems

Abstract

We pedagogically present the information theory as originally established, explaining its essential ideas and paying attention to the expression employed to measure the amount of information. Also we discussed relationships between information and quantum theories. In this context we determined the information entropies on position, S x , and momentum, S p , spaces, besides the entropy sum S t . Here, we use the modified entropic expressions that are dimensionally consistent. We provide original explanations for the behaviors of the S x , S p and S t values analyzing the probability densities and by means of the normalization constants and properties of Fourier transform. We validate the entropic uncertainty relation and inspect the standard deviation and information entropies as measures of quantum uncertainty. The systems of interest unidimensional one-particle quantum systems in ground and excited states.

Coulomb correlation and information entropies in confined helium-like atoms

“…These values correspond to regions where the probability densities are highly localized. This fact can also be observed in one-dimensional systems [14], in the spherically confined hydrogen atom [21] and systems with static screened Coulomb potential [72]. This result has a simple explanation in the quantum context [73]: when r c is reasonably small, the probability density becomes large and a 6 0 ρ(r 1 , r 2 ) > 1.…”

“…From the connection between information and quantum theories, it emerges the informational entropies in position, S r , and in momentum, S p , spaces, and the entropy sum S t by adding S r and S p . The study of quantum systems in information theory context already has a series of published works, for instance, analyses involving the one-dimensional systems [13][14][15][16][17] and confined hydrogen atom [18][19][20][21][22][23]. Studies on the free or confined helium-like atoms also have received attention in the informational context [24][25][26][27][28][29][30][31][32][33].…”

“…The S r and S p entropies are a type of dispersion or spread measures that are calculated without taking into account reference points in the probability distributions as Kennard's uncertainty relation (see, for example, Ref. [14] and references therein). In this sense, the entropic quantities are measures of uncertainty, localization or delocalization, of the wavefunction in the space [14,62].…”

“…[14] and references therein). In this sense, the entropic quantities are measures of uncertainty, localization or delocalization, of the wavefunction in the space [14,62].…”

Quantum-information theory of a Dirichlet ring with Aharonov-Bohm field

“…(6) 48,49 and work with the corresponding information-theoretic position and momentum lengths. Alternatively, by multiplying the logarithms' arguments in these definitions by the appropriate scale factor, one makes the functionals dimensionless [50][51][52][53][54] but, obviously, the values of S ρ and S γ depend in this case on the scale multiplier. Eqs.…”