Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models

Autor(en)

Tomasz Paterek, Borivoje Dakic, Caslav Brukner

Abstrakt

Mutually unbiased bases encapsulate the concept of complementarity—the impossibility of simultaneous knowledge of certain observables—in the formalism of quantum theory. Although this concept is at the heart of quantum mechanics, the number of these bases is unknown except for systems of dimension being a power of a prime. We develop the relation between this physical problem and the mathematical problem of finding the number of mutually orthogonal Latin squares. We derive in a simple way all known results about the unbiased bases, find their lower number, and disprove the existence of certain forms of the bases in dimensions different than power of a prime. Using the Latin squares, we construct hidden-variable models which efficiently simulate results of complementary quantum measurements.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Österreichische Akademie der Wissenschaften (ÖAW)

Journal

Physical Review A

Band

79

Anzahl der Seiten

6

ISSN

1050-2947

DOI

https://doi.org/10.1103/PhysRevA.79.012109

Publikationsdatum

2009

Peer-reviewed

Ja

ÖFOS 2012

103026 Quantenoptik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/b4d4c68c-d37c-472a-a29c-ea2d8eb6111a