The structure of qubit unextendible product bases
Nathaniel Johnston · Journal of Physics A Mathematical and Theoretical · 2014
Unextendible product bases (UPBs) have been shown to have many important uses in quantum information theory, particularly in the qubit case. However, very little is known about their mathematical structure beyond three qubits. We present several new results about qubit UPBs, including a complete characterization of all four-qubit UPBs, which we show there are exactly 1446 of. We also show that there exist p -qubit UPBs of almost all sizes less than 2 p . This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.