Geometry of quantum states: new construction of positive maps

TL;DR

This paper introduces a new class of positive maps for matrix algebras, based on geometric structures in quantum state space, generalizing the Choi map and aiding entanglement analysis.

Contribution

It presents a novel geometric construction of positive maps that extend the Choi map, offering new tools for quantum entanglement detection.

Findings

New class of positive maps derived from geometric balls in density matrix space

Generalizes the Choi map to a broader family of entanglement witnesses

Provides a versatile framework for analyzing quantum entanglement

Abstract

We provide a new class of positive maps in matrix algebras. The construction is based on the family of balls living in the space of density matrices of n-level quantum system. This class generalizes the celebrated Choi map and provide a wide family of entanglement witnesses which define a basic tool for analyzing quantum entanglement.