Method comparison: Time-independent and time-dependent coupling on qubitdyne protocol with higher photon states

Abstract

The qubitdyne protocol allows for quadrature detection of bosonic modes in stationary systems via repeated weak interactions with an auxiliary qubit. This approach circumvents the loss of photons in the cavity. While the earlier implementation of qubitdyne protocol utilizes constant coupling, Strandberg et al., suggests time-dependent coupling can significantly enhance the measurement process. In this study, we quantitatively analyze the efficiency of the qubitdyne protocol with constant and linearly increasing time-dependent couplings. The simulations were carried out with Fock, cat, and coherent states with increasing values of photons in the cavity (α = 4, 6, 8). The accuracy of the reconstruction was quantified by calculating the Kolmogorov-Smirnov (KS) statistic with respect to the ideal homodyne distributions. The results reveal that the constant coupling results in large deviations and high KS values up to ≈0.9 for the reconstructed quadrature distributions attributed to inefficiency in depleting the cavity. However, the time-dependent coupling results in low KS values (< 0.1) for all the reconstructed distributions. This reduces measurements by up to six times.