Fig. 4
Numerical simulation of the S-T0 qubit pure dephasing. a The return probabilities \(P_{|j\rangle }\left( {\tau _{\mathrm{s}}} \right)\) are measured by projecting the states onto each axis after a free induction decay time τs. Here, we show two numerical simulations at different J values. b The trajectories can be depicted in the Bloch sphere and the dynamics are therefore clearly visualized. The axes of rotation, as well as the angle Ω between the |S〉-axis, are identified by the normal vectors. c According to the rotation axes identified in (b), a unitary rotation \(\widehat R_\Omega\) recovers the standard form in Eq. (2). Then our procedure is applicable. The resulting \(\wp \left( \omega \right)\)’s reflect several physical intuitions, as explained in the main text. d The corresponding nonclassicality \({\cal{N}}\) at different J can be estimated according to Eq. (4). It increases with J in our simulation. In line with a realistic experimental modeling, statistically fluctuating noise is taken in account. The average nonclassicalities (brown dots) are reduced due to the noise. The brown error bars are the standard deviations of the series of nonclassicality \({\cal{N}}\) values obtained by repeatedly performing the noise simulation. More details are given in Supplementary Note 9
