Concavity of the quantum body for any given dimension

Details Concavity of the quantum body for any given dimension Concavity of the quantum body for any given dimension

2009-05-18

arxiv.org/abs/0905.2915v1

Phys. Rev. A 80, 042114 (2009)

Physics

Quantum Physics

5 pages, 1 figure

Scientific paper

Let us consider the set of all joint 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 joint 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 POVM allowed may contain points that can not be achieved with only projective measurements.

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