#### Alladi Ramakrishnan Hall

#### Unextendible k-separable bases and different inequivalent multipartite entangled subspace

#### Amit Mukherjee

##### IMSc

*ne of the most striking manifestations of quantum entanglement in multipartite scenario is in the form of Genuine Entanglement. It is therefore a very important question to find subspaces containing only genuine entanglement. Agarwal et al. [arXiv:1809.04202] have recently come up with genuinely entangled subspaces (GESs) in tripartite arbitrary dimensional system by introducing the notion of Unextendible Biseparable Bases (UBB). Moreover, they also constructed a GES which is bi-distillable, that is, all the states supported on that subspace are distillable across any bipartition. For scenarios considering more than three parties the question of Unextendible k-separable Bases (UKB) arises. In this ongoing work, we have introduced the notion of UKB and hence, the entangled subspace complimentary to UKB by generalising Agarwal et al.’s work for higher number of parties. We are also investigating some important open questions related to above notions.*

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