Research Article

Entropy of pure states: not all wave functions are born equal

Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia

^* Corresponding author: dks@phy.hr

Received: 16 September 2021
Accepted: 17 November 2021

Abstract

Many-body Hilbert space has the algebraic structure of a finitely generated free module. All N-body wave functions in d dimensions can be generated by a finite number of N!^d − 1 of generators called shapes, with symmetric-function coefficients. Physically the shapes are vacuum states, while the symmetric coefficients are bosonic excitations of these vacua. It is shown here that logical entropy can be used to distinguish fermion shapes by information content, although they are pure states whose usual quantum entropies are zero. The construction is based on the known algebraic structure of fermion shapes. It is presented for the case of N fermions in three dimensions. The background of this result is presented as an introductory review.