Unextendible product bases

DOI10.1006/jcta.2000.3122zbMath0985.15024OpenAlexW1988922918MaRDI QIDQ5940308

Noga Alon, László Lovász

Publication date: 29 July 2001

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcta.2000.3122

zbMATH Keywords

unextendible product basistensor productgraph connectivitygraph edge colouringsorthogonal vectorspure product vector

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Coloring of graphs and hypergraphs (05C15) Multilinear algebra, tensor calculus (15A69) Connectivity (05C40) Graph representations (geometric and intersection representations, etc.) (05C62)

Related Items (20)

Nonexistence of \(n\)-qubit unextendible product bases of size \(2^n-5\) ⋮ Strong quantum nonlocality for unextendible product bases in heterogeneous systems ⋮ Unextendible product basis for fermionic systems ⋮ The construction of 7-qubit unextendible product bases of size ten ⋮ Constructing unextendible product bases from multiqubit ones ⋮ Multipartite unextendible product bases and quantum security ⋮ On the structure of cube tilings and unextendible systems of cubes in low dimensions ⋮ Positively factorizable maps ⋮ Unextendible product bases and 1-factorization of complete graphs ⋮ Maximum dimension of subspaces with no product basis ⋮ Multiqubit UPB: the method of formally orthogonal matrices ⋮ The minimum size of unextendible product bases in the bipartite case (and some multipartite cases) ⋮ Constructing 2 × 2 × 4 and 4 × 4 unextendible product bases and positive-partial-transpose entangled states ⋮ A COMPLETELY ENTANGLED SUBSPACE OF MAXIMAL DIMENSION ⋮ Three-by-three bound entanglement with general unextendible product bases ⋮ Detecting quantum entanglement. ⋮ The unextendible product bases of four qubits: Hasse diagrams ⋮ \(4\times 4\) unextendible product basis and genuinely entangled space ⋮ Small set of orthogonal product states with nonlocality ⋮ Unextendible product bases from tile structures in bipartite systems

Uses Software

• QETLAB

Cites Work

• Unextendible product bases, uncompletable product bases and bound entanglement
• A correction: Orthogonal representations and connectivity of graphs
• Orthogonal representations and connectivity of graphs
• On the Shannon capacity of a graph
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