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arXiv · 1606.03878

Device-independent dimension tests in the prepare-and-measure scenario

Jamie Sikora·Antonios Varvitsiotis·Zhaohui Wei
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Abstract

Analyzing the dimension of an unknown quantum system in a device-independent manner, i.e., using only the measurement statistics, is a fundamental task in quantum physics and quantum information theory. In this paper, we consider this problem in the prepare-and-measure scenario. Specifically, we provide a lower bound on the dimension of the prepared quantum systems which is a function that only depends on the measurement statistics. Furthermore, we show that our bound performs well on several examples. {In particular}, we show that our bound provides new insights into the notion of dimension witness, and we also use it to show that the sets of restricted-dimensional prepare-and-measure correlations are not always convex.

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Jamie Sikora, Antonios Varvitsiotis, Zhaohui Wei. 2016-10-25. Device-independent dimension tests in the prepare-and-measure scenario. https://doi.org/10.1103/physreva.94.042125

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