Strong quantum nonlocality: Unextendible biseparability beyond unextendible product basis

An unextendible biseparable basis (UBB) is a set of orthogonal pure biseparable states which span a subspace of a given Hilbert space while the complementary subspace contains only genuinely entangled states. These biseparable bases are useful to produce genuinely entangled subspace in multipartite system. Such a subspace could be more beneficial for information theoretic applications if we are able to extract distillable entanglement across every bipartition from each state of this subspace. In this manuscript, we have derived a rule for constructing such a class of UBB which exhibits the phenomenon of strong quantum nonlocality. This result positively answers the open problem raised by Agrawal et al. [Phys. Rev. A 99, 032335 (2019)]; that there exists a UBB which can demonstrate the phenomenon of strong quantum nonlocality in the perspective of local irreducibility paradigm.
Comment: 15 pages, 4 figures, latex2e, comments welcome