Fig. 1

Skew information for the damped oscillator. Plot of quantum energetic fluctuations \(\sqrt {Q\left[ {\hat \pi _{\cal S},\hat E_{\cal S}^ \ast } \right]} {\mathrm{/}}\hbar \omega\) for the damped oscillator as a function of T/ħω for different coupling strengths γ. Here \(Q\left[ {\hat \pi _{\cal S},\hat E_{\cal S}^ \ast } \right]\) is the average Wigner-Yanase-Dyson skew information for the effective energy operator \(\hat E_{\cal S}^ \ast\). These fluctuations are present when the state of the oscillator \(\hat \pi _{\cal S}(T)\) is not diagonal in the basis of \(\hat E_{\cal S}^ \ast\) due to the non-negligible interaction between the system and reservoir. The plot shows that increasing the coupling γ leads to an increase in the skew information. The quantum fluctuations are most pronounced at low temperatures where the thermal energies become comparable to the oscillator spacing, \(T \simeq \hbar \omega\). As expected, the skew information decreases to zero in both the high temperature and weak coupling limits