Correction to: npj Quantum Information https://doi.org/10.1038/s41534-021-00415-0, published online 25 May 2021

The original version of this Article contained multiple errors in the caption of Fig. 3, in which “\(\gamma _ + ^ \circ\)” and “\(\gamma _ - ^ \circ\)” were incorrectly represented.

The first two sentences originally read “\(\gamma _0^ \circ\) (black), γ+ (red), and γ− (blue) corresponding to \(\epsilon \in \left( {0,\frac{\pi }{2}} \right)\): when \(0 \,< \,\epsilon \,< \frac{\,\pi }{4}\), \(\gamma _0^ \circ\) and Type = "math/tex">\gamma_{+}^{\circ} are positive. However, when \(\frac{\pi }{4} \le \epsilon \,< \frac{\pi }{2}\), \(\gamma _0^ \circ\) and Type = "math/tex">\gamma_{-}^\circ are non-positive”. The correct version reads “\(\gamma _0^ \circ\)(black), \(\gamma _ + ^ \circ\)(red), and \(\gamma _ - ^ \circ\)(blue) corresponding to \(\epsilon \in \left( {0,\frac{\pi }{2}} \right)\): when \(0 \,< \,\epsilon \,< \,\frac{\pi }{4}\), \(\gamma _0^ \circ\) and \(\gamma _ + ^ \circ\) are positive. However, when \(\frac{\pi }{4} \,\le \,\epsilon \,< \,\frac{\pi }{2}\), \(\gamma _0^ \circ\) and \(\gamma _ - ^ \circ\) are non-positive.”

This has been corrected in both the PDF and HTML versions of the Article.