| Issue |
4open
Volume 5, 2022
Logical Entropy
|
|
|---|---|---|
| Article Number | 3 | |
| Number of page(s) | 10 | |
| Section | Physics - Applied Physics | |
| DOI | https://doi.org/10.1051/fopen/2021006 | |
| Published online | 25 January 2022 | |
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
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.
Key words: Many-body Hilbert space / Free module / Logical entropy / Quantum entropy / Bargmann space
© D.K. Sunko, Published by EDP Sciences, 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.