Entanglement in mutually unbiased bases

Autor(en)

Marcin Adam Wiesniak, Tomasz Paterek, Anton Zeilinger

Abstrakt

One of the essential features of quantum mechanics is that most pairs of observables cannot be measured simultaneously. This phenomenon manifests itself most strongly when observables are related to mutually unbiased bases. In this paper, we shed some light on the connection between mutually unbiased bases and another essential feature of quantum mechanics, quantum entanglement. It is shown that a complete set of mutually unbiased bases of a bipartite system contains a fixed amount of entanglement, independent of the choice of the set. This has implications for entanglement distribution among the states of a complete set. In prime-squared dimensions we present an explicit experiment-friendly construction of a complete set with a particularly simple entanglement distribution. Finally, we describe the basic properties of mutually unbiased bases composed of product states only. The constructions are illustrated with explicit examples in low dimensions. We believe that the properties of entanglement in mutually unbiased bases may be one of the ingredients to be taken into account to settle the question of the existence of complete sets. We also expect that they will be relevant to applications of bases in the experimental realization of quantum protocols in higher-dimensional Hilbert spaces.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

University of Gdańsk

Journal

New Journal of Physics

Band

13

Anzahl der Seiten

24

ISSN

1367-2630

DOI

https://doi.org/10.1088/1367-2630/13/5/053047

Publikationsdatum

2011

Peer-reviewed

Ja

ÖFOS 2012

103026 Quantenoptik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/7c8eca32-6cae-460f-a562-e4465c313f0c