An algorithm to explore entanglement in small systems

TL;DR

This paper introduces a simple iterative algorithm based on Schmidt decompositions to explore and optimize entanglement properties in small quantum systems, applicable to various entanglement measures and quantum state analyses.

Contribution

The paper presents a novel, straightforward iterative algorithm that maximizes or minimizes Schmidt norms to analyze entanglement in small quantum systems, accommodating multiple bipartite cuts and subspace constraints.

Findings

Algorithm reliably converges to local optima.

Applied to fermionic states and quantum channels, revealing entanglement characteristics.

Facilitates exploration of maximally entangled states and entropy minimization.

Abstract

A quantum state's entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms. Depending on the choice of norm, the optimizing states maximize or minimize entanglement, possibly across several bipartite cuts at the same time and possibly only among states in a specified subspace. Recognizing that convergence but not success is certain, we use the algorithm to explore topics ranging from fermionic reduced density matrices and varieties of pure quantum states to absolutely maximally entangled states and minimal output entropy of channels.