A geometric comparison of entanglement and quantum nonlocality in discrete systems

Abstract

We compare entanglement with quantum nonlocality employing a geometric structure of the state space of bipartite qudits. 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 shown that also for mixtures of states sharing the same amount of entanglement, Bell inequality violations and entanglement measures are non-monotonically related.

20 pages, 7 figures, published version

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• Heisenberg's Uncertainty Relation and Bell Inequalities in High Energy Physics
• Examining the dimensionality of genuine multipartite entanglement
• Bell violation versus geometric measure of quantum discord and their dynamical behavior
• Bipartite Bound Entanglement
• Investigating nonclassicality of many qutrits by symmetric two-qubit operators
• The Entropic Uncertainty Principle for Decaying Systems and CP violation