Bipartite entanglement of quantum states in a pair basis

TL;DR

This paper introduces a new class of quantum states called pair basis states, enabling efficient bipartite entanglement measurement in higher dimensions, with exact negativity criteria and bounds for entanglement of formation.

Contribution

It identifies pair basis states as a class allowing exact negativity-based entanglement detection and provides analytical bounds for entanglement of formation.

Findings

Negativity is necessary and sufficient for entanglement in pair basis states.

Analytical expressions for lower bounds of entanglement of formation.

Relevance of pair basis states in quantum optics and higher-dimensional systems.

Abstract

The unambiguous detection and quantification of entanglement is a hot topic of scientific research, though it is limited to low dimensions or specific classes of states. Here we identify an additional class of quantum states, for which bipartite entanglement measures can be efficiently computed, providing new rigorous results. Such states are written in arbitrary $d\times d$ dimensions, where each basis state in the subsystem A is paired with only one state in B. This new class, that we refer to as pair basis states, is remarkably relevant in many physical situations, including quantum optics. We find that negativity is a necessary and sufficient measure of entanglement for mixtures of states written in the same pair basis. We also provide analytical expressions for a tight lower-bound estimation of the entanglement of formation, a central quantity in quantum information.