A geometric comparison of entanglement and quantum nonlocality in discrete systems

Autor(en)
Christoph Spengler, Marcus Huber, Beatrix Hiesmayr
Abstrakt

We compare entanglement with quantum nonlocality employing a geometric structure of the state space of bipartite qudits. The central object is a regular simplex spanned by generalized Bell states. The Collins-Gisin-Linden-Massar-Popescu-Bell inequality is used to reveal states of this set that cannot be described by local-realistic theories. Optimal measurement settings necessary to ascertain nonlocality are determined by means of a recently proposed parameterization of the unitary group U(d) combined with robust numerical methods. The main results of this paper are descriptive geometric illustrations of the state space that emphasize the difference between entanglement and quantum nonlocality. Namely, it is found that the shape of the boundaries of separability and Bell inequality violation are essentially different. Moreover, it is also shown that for mixtures of states sharing the same amount of entanglement, Bell inequality violations and entanglement measures are non-monotonically related.

Organisation(en)
Teilchenphysik
Journal
Journal of Physics A: Mathematical and Theoretical
Band
44
Anzahl der Seiten
18
ISSN
1751-8113
DOI
https://doi.org/10.1088/1751-8113/44/6/065304
Publikationsdatum
2011
Peer-reviewed
Ja
ÖFOS 2012
103025 Quantenmechanik
Link zum Portal
https://ucrisportal.univie.ac.at/de/publications/a-geometric-comparison-of-entanglement-and-quantum-nonlocality-in-discrete-systems(f01d9c09-c067-46a3-815f-e8bf2901f436).html