Construction of quantum states with special properties by projection methods

TL;DR

This paper develops projection-based algorithms to construct quantum states with specific properties, such as prescribed marginals, eigenvalues, rank, and entropy, providing new insights through numerical experiments.

Contribution

It introduces novel algorithms using convex analysis and optimization on matrix manifolds for constructing quantum states with desired properties.

Findings

Algorithms successfully generate quantum states with prescribed marginals and properties.

Numerical results reveal new patterns and insights in quantum state construction.

The methods open new research directions in quantum information theory.

Abstract

We use projection methods to construct (global) quantum states with prescribed reduced (marginal) states, and possibly with some special properties such as having specific eigenvalues, having specific rank and extreme von Neumann or Renyi entropy. Using convex analysis, optimization techniques on matrix manifolds, we obtain algorithms to solve the problem. Matlab programs are written based on these algorithms and numerical examples are illustrated. The numerical results reveal new patterns leading to new insights and research problems on the topic.