Correction to: Nature Communications https://doi.org/10.1038/s41467-017-02511-2, published online 15 January 2018

In the original version of this Article, the penultimate sentence of the second paragraph of the “Schematic and theory” section of the Results originally incorrectly read “For instance, choosing θA = π/4, 0, −π/8 and π/8 rotates the bases \(\left| 0 \right\rangle\), \(\left| 1 \right\rangle\), \(\left| + \right\rangle\), and \(\left| - \right\rangle\) into \(\left| 1 \right\rangle\), thereby implementing the observable \(\hat A = \left| 0 \right\rangle \left\langle 0 \right|\), \(\left| 1 \right\rangle\)\(\left\langle 1 \right|\), \(\left| + \right\rangle\)\(\left\langle + \right|\) and, respectively.” In the corrected version, “\(\left| - \right\rangle\)\(\left\langle - \right|\)” has been added before “, respectively”. This error has been corrected in both the PDF and HTML versions of the Article.