Enhancing the Size of Phase-Space States Containing Sub-Planck-Scale Structures via Non-Gaussian Operations

We observe a metrological advantage in phase-space sensitivity for photon-added cat and kitten states over their original forms, due to phase-space broadening from increased amplitude via photon addition, albeit with higher energy cost. Using accessible non-classical resources, weak squeezing and displacement, we construct a squeezed state and two superposed states: the squeezed cat state and the symmetrically squeezed state. Their photon-added variants are compared with parity-matched cat and KSs using quantum Fisher information and fidelity. The QFI isocontours reveal regimes where KS exhibit high fidelity and large amplitude, enabling their preparation via Gaussian operations and photon addition. Similar regimes are identified for cat states enhanced by squeezing and photon addition, demonstrating improved metrological performance. Moreover, increased amplitude and thus larger phase-space area reduces the size of interferometric fringes, enhancing the effectiveness of quantum error correction in cat codes.