Despite a lot of effort, numerical or exact fiducial vectors are only known for a finite, though growing list of dimensions. Byczkowski, "Hiperboliczny proces stabilny. These are length one chain complexes over a finite field. Specyficzne miejsce sekwencji DNA na chromosomie zwane jest locus. Nie mieszają się w czasie rozrodu z genami innych organizmów.
It has been conjectured that SIC-POVMs exist for all dimensions and that they can be constructed as orbits of a so-called fiducial vector under the Weyl-Heisenberg group.
Despite a lot of effort, numerical or exact fiducial vectors are only known for a finite, though growing list of dimensions. Currently, numerical ones have been found for all dimensions up to Solutions in larger dimensions have been found as part of conjectured families obeying additional symmetries.
Links to number-theoretic conjectures in this context allow to convert numerical solutions of moderate precision into exact solutions, including dimensions and This allows us to provide an example of a quantum engine whose favorable power output scaling unavoidably requires nonclassical effects in the form of contextuality. Furthermore, we describe contextual advantages for local metrology.
Given the ubiquity of linear response theory, we anticipate that these tools will allow one to certify the nonclassicality of a wide array of quantum phenomena. These are length one chain complexes over a finite field. Quantum CSS stabilizer codes can be seen as length two or more chain complexes over a finite field.
There are no complex numbers to be seen here, so what is quantum about quantum codes? One possible answer is that these codes, as chain complexes, live in a symmetric closed monoidal category enriched over itself.
This also applies to the category of finite dimensional complex vector spaces, the usual context in which we do quantum information theory. In this talk I Hidden Markow Model Trading Strategia discuss these parallels using string diagram notation.
As might be suspected, they key is the behaviour of the tensor product in both contexts. Recently, several approaches towards its quantum version have been developed. In the talk I will provide an overview of the quantum optimal transport problem basing on the recent joint work arXiv The general results will be illustrated with a more detailed study of the single-qubit transport problem.
In particular, I will show that the quantum Hidden Markow Model Trading Strategia transport induces a new metric on the Bloch ball with intriguing properties.