General Depolarized Pure States: Identification and Properties

TL;DR

This paper introduces a generalized Schmidt decomposition for depolarized pure states, providing new methods for their identification and insights into their eigenvalue structure, with implications for quantum entanglement analysis.

Contribution

It presents a novel generalized Schmidt decomposition applicable to depolarized pure states and offers experimental identification techniques for this class of mixed states.

Findings

New generalized Schmidt decomposition for depolarized pure states

Experimental methods for identifying these states

Interpretation of negative eigenvalues in density matrices

Abstract

The Schmidt decomposition is an important tool in the study of quantum systems especially for the quantification of the entanglement of pure states. However, the Schmidt decomposition is only unique for bipartite pure states, and some multipartite pure states. Here a generalized Schmidt decomposition is given for states which are equivalent to depolarized pure states. Experimental methods for the identification of this class of mixed states are provided and some examples are discussed which show the utility of this description. A particularly interesting example provides, for the first time, an interpretation of the number of negative eigenvalues of the density matrix.