Higher-Order-Schmidt-Representations and their Relevance for the Basis-Ambiguity

TL;DR

This paper explores higher-order Schmidt representations using polar decomposition of operators, clarifying their properties and relation to tensor-product states, which enhances understanding of basis ambiguity in quantum systems.

Contribution

It introduces a unified framework for higher-order Schmidt representations leveraging polar decomposition, linking tensor-product states and compact operators.

Findings

Provides a compact account of properties of higher-order Schmidt representations

Establishes a unique relation between tensor-product states and compact operators

Enhances understanding of basis ambiguity in quantum mechanics

Abstract

With the help of a useful mathematical tool, the polar decomposition of closed operators, and a simple observation, i.e. the unique relation between tensor-product states and compact operators, we manage to give a compact and coherent account of the various properties of higher-order-Schmidt-representations.