Minimum Cardinalities of Multipartite Unextendible Product Bases

In quantum information theory, the state space of a multipartite quantum system is modeled by a tensor product. In the tensor-product space $\mathbb C^{d_1}\otimes\cdots\otimes\mathbb C^{d_p}$, a nonzero vector is a \emph{product state} if it can be written as $\lvert φ_1\rangle\otimes\cdots\otimes\