The Minimum Size of Qubit Unextendible Product Bases

Abstract

We investigate the problem of constructing unextendible product bases in the qubit case - that is, when each local dimension equals 2. The cardinality of the smallest unextendible product basis is known in all qubit cases except when the number of parties is a multiple of 4 greater than 4 itself. We construct small unextendible product bases in all of the remaining open cases, and we use graph theory techniques to produce a computer-assisted proof that our constructions are indeed the smallest possible.

13 pages, 13 figures

References in corpus (2)

• Tight Bell inequalities with no quantum violation from qubit unextendible product bases
• Locally Indistinguishable Subspaces Spanned by Three-Qubit Unextendible Product Bases

Cited by in corpus (15)

• The Minimum Size of Unextendible Product Bases in the Bipartite Case (and Some Multipartite Cases)
• Nonlocal sets of orthogonal product states in arbitrary multipartite quantum system
• The Structure of Qubit Unextendible Product Bases
• Exploring the Local Orthogonality Principle
• Strongly nonlocal unextendible product bases do exist
• Strong quantum nonlocality for unextendible product bases in heterogeneous systems
• Unextendible Product Basis for Fermionic Systems
• Local distinguishability of quantum states in multipartite System
• Unextendible and strongly uncompletable product bases
• Constructing $2\times 2\times 4$ and $4\times 4$ unextendible product bases and positive-partial-transpose entangled states
• The construction and local distinguishability of multiqubit unextendible product bases
• Constructing unextendible product bases from multiqubit ones
• The unextendible product bases of four qubits: Hasse diagrams
• Novel methods to construct nonlocal sets of orthogonal product states in arbitrary bipartite high-dimensional system
• $4\times 4$ unextendible product basis and genuinely entangled space