### 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 |

Volume | 80 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 30 2009 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

**Concavity of the set of quantum probabilities for any given dimension.** / Pál, K.; Vértesi, T.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 80, no. 4, 042114. https://doi.org/10.1103/PhysRevA.80.042114

}

TY - JOUR

T1 - Concavity of the set of quantum probabilities for any given dimension

AU - Pál, K.

AU - Vértesi, T.

PY - 2009/10/30

Y1 - 2009/10/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70350751576&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350751576&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.80.042114

DO - 10.1103/PhysRevA.80.042114

M3 - Article

VL - 80

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 4

M1 - 042114

ER -