Multiqubit UPB: the method of formally orthogonal matrices
Abstract
We use formal matrices whose entries we view as vector variables taking unit vector values in onequbit Hilbert spaces of a multiqubit quantum system. We construct many unextendible product bases (UPBs) of new sizes in such systems and provide a new construction of UPBs of n qubits of cardinality n + 1 when . We also give a new method of constructing multiqubit entangled states with all partial transposes positive.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 June 2018
 DOI:
 10.1088/17518121/aac53b
 arXiv:
 arXiv:1801.08677
 Bibcode:
 2018JPhA...51z5302C
 Keywords:

 Quantum Physics
 EPrint:
 19 pages, the example in Appendix B corrected