Between the 5th and the 20th of March, Dr. Dardo Goyeneche, researcher of the Optics and Quantum Information Division, realized a research stay at the University of York (England). There, together with Dr. Stefan Weigert, they worked on the algorithm that the CEFOP researcher designed during his doctoral thesis. The main application of this algorithm is the search for Mutually Complementary Bases (MU bases, in its English abbreviation) in spaces of arbitrary dimension. During his stay, he made use of the supercomputers of the “White Rose Grid”, to which the University of York belongs. This implies the ability to obtain in just a short time results that would take months to obtain on an individual computer, and allows the study of the problem in much higher dimensions than those currently explored.
It is known that in d-dimensional complex spaces it is possible to construct d+1 mutually complementary bases when d is of prime power. In other dimensions the problem remains open, d=6 being the first case where answers are not known. This algorithm efficiently finds the maximum set of MU bases that can be constructed from a pair of given MU bases, in all dimensions.
Dr. Stefan Weigert is full professor of the Mathematics Department at the University of York and a referee of prestigious scientific journals. In addition, he is a world-class expert on the study of Hadamard matrices and MU bases, with more than 20 years of experience in the field.
The problem of the existence of mutually complementary d+1 bases in all d-dimensional space is recognized as one of the more important open problems of the Theory of Quantum Information. Its important applications in quantum state tomography, quantum key distribution, dense coding, teleportation, entanglement swapping, covariant cloning, among others, have attracted the interest of many researchers in the last two decades. “Richard Feynman said that nobody understands quantum mechanics. If the existence of these maximum sets of mutually complementary bases could be demonstrated in all dimensions, we would be a step closer to understanding it,” Dardo claims.