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Experimental device-independent tests of classical and quantum dimensions

Nature Physics volume 8, pages 592–595 (2012)Cite this article

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Abstract

A fundamental resource in any communication and computation task is the amount of information that can be transmitted and processed. The classical information encoded in a set of states is limited by the number of distinguishable states or classical dimension dc of the set. The sets used in quantum communication and information processing contain states that are neither identical nor distinguishable, and the quantum dimension dq of the set is the dimension of the Hilbert space spanned by these states. An important challenge is to assess the (classical or quantum) dimension of a set of states in a device-independent way, that is, without referring to the internal working of the device generating the states. Here we experimentally test dimension witnesses designed to efficiently determine the minimum dimension of sets of (three or four) photonic states from the correlations originated from measurements on them, and distinguish between classical and quantum sets of states.

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Figure 1: Device-independent scenario for testing the minimum classical or quantum dimension.
Figure 2: Experimental set-up for testing classical and quantum dimension witnesses.
Figure 3: Experimental results of the dimension witness tests.

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Acknowledgements

The authors thank A. Acín, E. Amselem and R. Gallego for stimulating discussions. This work was supported by the Swedish Research Council (VR), the Linnaeus Center of Excellence ADOPT, the MICINN Project No. FIS2008-05596 and the Wenner-Gren Foundation.

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Authors and Affiliations

  1. Physics Department, Stockholm University, S-10691 Stockholm, Sweden

    Johan Ahrens, Piotr Badzia̧g, Adán Cabello & Mohamed Bourennane

  2. Departamento de Fı´sica Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain

    Adán Cabello

Authors
  1. Johan Ahrens
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  2. Piotr Badzia̧g
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  3. Adán Cabello
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  4. Mohamed Bourennane
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Contributions

J.A. carried out the experiments under M.B.’s supervision. P.B., A.C. and M.B. jointly conceived the experiments. All authors analysed the data and wrote the manuscript.

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Correspondence to Mohamed Bourennane.

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The authors declare no competing financial interests.

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Ahrens, J., Badzia̧g, P., Cabello, A. et al. Experimental device-independent tests of classical and quantum dimensions. Nature Phys 8, 592–595 (2012). https://doi.org/10.1038/nphys2333

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