Abstract
Shannon quantum information entropies S_ρ,γ, Fisher informations I_ρ,γ, Onicescu energies O_ρ,γ and complexities e^SO are calculated both in position (subscript ρ) and momentum (γ) spaces for azimuthally symmetric 2D nanoring that is placed into combination of transverse uniform magnetic field B and Aharonov-Bohm (AB) flux φ_AB and whose potential profile is modeled by superposition of quadratic and inverse quadratic dependencies on radius r. Increasing intensity B flattens momentum waveforms Φ_nm( k) and in the limit of infinitely large fields they turn to zero, what means that the position wave functions Ψ_nm( r), which are their Fourier counterparts, tend in this limit to the δ-functions. Position (momentum) Shannon entropy depends on the field B as a negative (positive) logarithm of ω_eff≡(ω₀²+ω_c²/4)^1/2, where ω₀ determines the quadratic steepness of the confining potential and ω_c is a cyclotron frequency. This makes the sum S_ρ_nm+S_γ_nm a field-independent quantity that increases with the principal n and azimuthal m quantum numbers and does satisfy entropic uncertainty relation. Position Fisher information does not depend on m, linearly increases with n and varies as ω_eff whereas its n and m dependent Onicescu counterpart O_ρ_nm changes as ω_eff⁻¹. The products I_ρ_nmI_γ_nm and O_ρ_nmO_γ_nm are B-independent quantities. A dependence of the measures on the ring geometry is discussed. It is argued that a variation of the position Shannon entropy or Onicescu energy with the AB field uniquely determines an associated persistent current as a function of φ_AB at B=0. An inverse statement is correct too.