Research ArticlePHYSICS

Self-testing nonprojective quantum measurements in prepare-and-measure experiments

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Science Advances  17 Apr 2020:
Vol. 6, no. 16, eaaw6664
DOI: 10.1126/sciadv.aaw6664
  • Fig. 1 Graphical overview of the self-testing methods and steps presented in Results.

  • Fig. 2 Method for self-testing a targeted nonprojective qubit measurement by exploiting simpler self-tests of preparations.

    Step 1: tailor scenario and witness such that a maximal A self-tests Alice’s preparations to have Bloch vectors that are anti-aligned with those of the target measurement. Step 2: Add an extra setting to Bob and modify the witness to self-test the target non-projective measurement.

  • Fig. 3 Numerical approximation of the worst-case fidelity of the unknown measurement (setting povm) with the qubit SIC-POVM by roughly 3×105 random three- and four-outcome POVM samples for which the optimal values of (A,F) were calculated.

    The figure also displays the critical limits on ASIC and F for projective and three-outcome POVMs, respectively, as well as the experimentally measured values.

  • Fig. 4 Lower bound on (Atri) for k=1 obtained from the swap method, together with roughly 3000 points (Atri,) obtained via the numerical approximation method.

    This is displayed next to the experimentally achieved results.

  • Fig. 5 Experimental setup.

    More details, including labeling, can be found in the main text. Pol, polarizer.

Supplementary Materials

  • Supplementary Materials

    Self-testing nonprojective quantum measurements in prepare-andmeasure experiments

    Armin Tavakoli, Massimiliano Smania, Tamás Vértesi, Nicolas Brunner, Mohamed Bourennane

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    • Sections S1 to S5
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