Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition

TL;DR

This paper introduces a method to construct genuinely entangled subspaces in multipartite quantum systems that contain distillable entanglement across all bipartitions, advancing quantum information applications.

Contribution

It presents a novel approach using unextendible biseparable bases to explicitly construct genuinely entangled subspaces with all-encompassing distillable entanglement.

Findings

Constructed UBBs for 3-qudit systems with local dimension d≥3.

Demonstrated the resulting GES is bidistillable across all bipartitions.

Provided explicit examples of symmetric and asymmetric UBBs.

Abstract

In a multipartite scenario quantum entanglement manifests its most dramatic form when the state is genuinely entangled. Such a state is more beneficial for information theoretic applications if it contains distillable entanglement in every bipartition. It is, therefore, of significant operational interest to identify subspaces of multipartite quantum systems that contain such properties apriori. In this letter, we introduce the notion of unextendible biseparable bases (UBB) that provides an adequate method to construct genuinely entangled subspaces (GES). We provide an explicit construction of two types of UBBs -- party symmetric and party asymmetric -- for every $3$-{\it qudit} quantum system, with local dimension d\ge 3. Further, we show that the GES resulting from the symmetric construction is indeed a {\it bidistillable} subspace, i.e., all the states supported on it contain distillable entanglement across every bipartition.