Dilation Theoretic Parametrizations of Positive Matrices with Applications to Quantum Information

TL;DR

This paper explores two parametrizations of positive matrices, with applications in quantum information, including constructing separable states and providing an alternative qubit representation.

Contribution

It introduces and applies the Schur-Constantinescu and Jacobi parametrizations to quantum states and qubits, offering new tools for quantum information analysis.

Findings

Constructed examples of separable states using the Schur-Constantinescu parametrization.

Presented an alternative to the Bloch sphere for qubit representation.

Demonstrated the utility of these parametrizations in quantum information theory.

Abstract

This paper, dedicated to the memory of late Professor Tiberiu Constantinescu, discusses two parametrizations of positive matrices. The first, called the Schur-Constantinescu parametrization, is used to construct several examples of separable states (e.g., Hankel states). The second, called the Jacobi parametrization, is used to present an alternative to the Bloch sphere representation of qubits.