A genuinely unextendible product basis with precisely fourteen elements now exists, definitively resolving a long-standing question in quantum information theory. Prior work established a lower bound of thirteen states, but this construction proves fourteen is the minimum cardinality for a three-qutrit system. This result extends to all tripartite systems utilising local dimensions of at least three.
Researchers Find Minimum Size for Quantum Basis
A genuinely unextendible product basis with precisely fourteen elements now exists, definitively resolving a long-standing question in quantum information theory. Prior work established a lower bound of thirteen states, but this construction proves fourteen is the minimum cardinality for a three-qutrit system. This result extends to all tripartite systems utilising local dimensions of at least three.