Bipartite Entanglement Review of Subsystem-Basis Expansions and Correlation Operators in It

TL;DR

This review revisits previous results on bipartite entanglement, presenting them with standard techniques to enhance clarity and impact, and summarizes key theorems and propositions related to subsystem-basis expansions and correlation operators.

Contribution

The paper re-derives earlier findings using standard methods, making the results more accessible and better integrated into existing literature.

Findings

Derivation of key theorems on bipartite entanglement

Clarification of correlation operators in subsystem-basis expansions

Use of partial scalar product and trace methods

Abstract

The present review presents the authors previous results on the topic from the title in a new light. Most of the previous results were obtained using the techniques of antilinear Hilbert-Schmidt mappings of one Hilbert pace into another, which is unknown and unused in the literature. This, naturally, diminished the impact of the results. In this article the results are derived anew with standard techniques. The topics listed at the end of the Introduction, are expounded in 9 theorems, 5 propositions etc. Partial scalar product and partial trace methods are used throughout. Further relevant research articles that are not reproduced in this review, are sketched in the Concluding remarks.