  Anomalous weak values and Wigner function's negativity are well known
witnesses of quantum contextuality. We show that these effects occur when
analyzing the energetics of a single qubit gate generated by a resonant
coherent field traveling in a waveguide. The buildup of correlations between
the qubit and the field is responsible for bounds on the gate fidelity, but
also for a nontrivial energy balance recently observed in a superconducting
setup. In the experimental scheme, the field is continuously monitored through
heterodyne detection and then post-selected over the outcomes of a final
qubit's measurement. The post-selected data can be interpreted as field's weak
values and can show anomalous values in the variation of the field's energy. We
model the joint system dynamics with a collision model, gaining access to the
qubit-field entangled state at any time. We find an analytical expression of
the quasi-probability distribution of the post-selected heterodyne signal, i.e.
the conditional Husimi-Q function. The latter grants access to all the field's
weak values: we use it to obtain that of the field's energy change and display
its anomalous behaviour. Finally, we derive the field's conditional Wigner
function and show that anomalous weak values and Wigner function's negativities
arise for the same values of the gate's angle.
