Mapping Criteria of Nonlocality-Steerability in Qudit-Qubit Systems and Steerability-Entanglement in Qubit-Qudit Systems

TL;DR

This paper develops analytical mapping criteria between nonlocality, steering, and entanglement in bipartite qudit-qubit and qubit-qudit systems, clarifying their quantitative relationships in quantum correlations.

Contribution

It introduces state-independent analytical mapping criteria between different quantum correlations in bipartite systems, unifying and extending previous results.

Findings

Derived explicit mapping criteria between Bell nonlocality and quantum steering.

Established mapping between quantum steering and entanglement.

Criteria are independent of the specific quantum state form.

Abstract

Entanglement, quantum steering and nonlocality are distinct quantum correlations which are the resources behind various of quantum information and quantum computation applications. However, a central question of determining the precise quantitative relation among them is still unresolved. Here, we present a mapping criterion between Bell nonlocality and quantum steering in bipartite qudit-qubit system, as well as a mapping criterion between quantum steering and quantum entanglement in bipartite qubit-qudit system, starting from the fundamental concepts of quantum correlations. Precise quantitative mapping criteria are derived analytically. Such mapping criteria are independent of the form of the state. In particular, they cover several previous well-known research results which are only special cases in our simple mapping criteria.