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How many orthonormal bases are needed to distinguish all pure quantum states?

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Abstract

We collect some recent results that together provide an almost complete answer to the question stated in the title. For the dimension d = 2 the answer is three. For the dimensions d = 3 and d ≥ 5 the answer is four. For the dimension d = 4 the answer is either three or four. Curiously, the exact number in d = 4 seems to be an open problem.

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Authors and Affiliations

  1. DIME, Università di Genova, Via Magliotto 2, 17100, Savona, Italy

    Claudio Carmeli

  2. Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, Turku, Finland

    Teiko Heinosaari & Jussi Schultz

  3. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy

    Jussi Schultz & Alessandro Toigo

  4. Sezione di Milano, I.N.F.N., Via Celoria 16, 20133, Milano, Italy

    Alessandro Toigo

Authors
  1. Claudio Carmeli
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  2. Teiko Heinosaari
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  3. Jussi Schultz
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  4. Alessandro Toigo
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Correspondence to Teiko Heinosaari.

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Carmeli, C., Heinosaari, T., Schultz, J. et al. How many orthonormal bases are needed to distinguish all pure quantum states?. Eur. Phys. J. D 69, 179 (2015). https://doi.org/10.1140/epjd/e2015-60230-5

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  • DOI: https://doi.org/10.1140/epjd/e2015-60230-5

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