### Abstract

Let us consider the set of all probabilities generated by local binary measurements on two separated quantum systems of a given local dimension d. We address the question of whether the shape of this quantum body is convex or not. We construct a point in the space of probabilities, which is on the convex hull of the local polytope, but still cannot be attained by measuring d -dimensional quantum systems if the number of measurement settings is large enough. From this it follows that this body is not convex. We also show that for finite d the quantum body with the generalized measurement associated with positive operator-valued measures allowed may contain points that cannot be achieved with only projective measurements.

Original language | English |
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Article number | 042114 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 80 |

Issue number | 4 |

DOIs | |

Publication status | Published - okt. 30 2009 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics