Genuinely entangled subspaces and strongly nonlocal unextendible biseparable bases in four-partite systems

TL;DR

This paper constructs strongly nonlocal unextendible biseparable bases in four-partite qudit systems, creating genuinely entangled subspaces that are distillable across all bipartitions, advancing quantum nonlocality and information processing.

Contribution

It introduces a new method for constructing strongly nonlocal UBBs in four-partite systems and demonstrates their distillability and specific basis structures.

Findings

Constructed strongly nonlocal UBBs in 4-qudit systems

Demonstrated distillability of entangled subspaces across all bipartitions

Provided explicit orthonormal bases for some entangled subspaces

Abstract

A set of orthogonal pure states is an unextendible biseparable basis (UBB), which means that its complementary subspace contains only genuinely entangled states. UBBs thus serve as an effective tool for constructing genuinely entangled subspaces. If every state within such a subspace exhibits distillable entanglement across all bipartitions, it becomes particularly advantageous for applications in quantum information. In this paper, we mainly conduct research on the 4-qudit quantum systems, where the local dimension $d$ is not less than 3. We present an approach for constructing UBB and prove that the UBB established in this way is strongly nonlocal. We build several genuinely entangled subspaces and demonstrate the distillability of the genuinely entangled subspaces across all bipartitions. In addition, we also describe the specific orthonormal basis for some genuinely entangled subspaces. These results will not only contribute to the development of quantum nonlocality theory, but also provide a crucial theoretical foundation for practical quantum information processing tasks.