Nonexistence of $n$-qubit unextendible product bases of size $2^n-5$

Abstract

It is known that the $n$-qubit system has no unextendible product bases (UPBs) of cardinality $2^n-1$, $2^n-2$ and $2^n-3$. On the other hand the $n$-qubit UPBs of cardinality $2^n-4$ exist for all $n\ge 3$. We prove that they do not exist for cardinality $2^n-5$.

6 pages

References in corpus (1)

• Qubit-qudit states with positive partial transpose

Cited by in corpus (4)

• Unextendible product bases from tile structures and their local entanglement-assisted distinguishability
• Negative result about the construction of genuinely entangled subspaces from unextendible product bases
• Constructing unextendible product bases from multiqubit ones
• Progress in the study of the (non)existence of genuinely unextendible product bases