Joint optimization of the probing schedule under frequency uncertainty and dissipation

Optimize the probing-time schedule jointly against the calibrated or worst-case noisy dynamics, including the thermal-relaxation dynamics with bounded frequency uncertainty, to determine whether and by how much the certifiable regions can be widened.

Background

The protocol fixes the three probing times at t_k = kT_0/3, inherited from the noiseless harmonic-oscillator protocol. In the presence of dissipation and uncertainty in the actual precession frequency, the valid classical and Wigner-positivity thresholds must instead account for the admissible noisy dynamics, including the worst case over the frequency uncertainty interval.

The paper explicitly identifies the probing schedule as an unused degree of freedom and leaves open its joint optimization against the calibrated or worst-case noisy dynamics. Such an optimization is motivated by the expectation that adapting the measurement times could enlarge the certifiable regions for nonclassicality and Wigner negativity.