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

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.

Evaluation and spanning sets of confluent Vandermonde forms

“…One can organize the complete set of generators in a lattice connected by the non-zero operations of symmetrized derivatives. 18 The subset of generalized-harmonic generators are the non-zero end-points of that procedure, like a rim, which can thus be naturally connected to the zero polynomial as bottom of the lattice. In the above example, the rim consists of the three generators (57), each connected to Ψ 4 with a line representing an operation like (59).…”

Logical entropy – special issue

“…The paper by Denis Sunko [8] addresses the logical entropy in the context of many-body quantum mechanics. It shows how the logical entropy can be used to distinguish many-body fermion states by their information content, although they are pure states whose usual quantum entropies are equal to zero.…”