Tomographic measurement data of states that never existed

Microscopic Schr{\"o}dinger cat states are generated from quantum correlated fields using a probabilistic heralding photon subtraction event. Subsequent quantum state tomography provides complete information about the state with typical photon numbers of the order of one. Another approach strives for a larger number of quantum-correlated photons by conditioning the measurement analysis on events with exactly this number of photons. Here, we present a new approach to derive measurement data of quantum correlated states with average quantum-correlated photon numbers significantly larger than one. We produce an ensemble of a heralded, photon-subtracted squeezed vacuum state of light. We split the states at a balanced beam splitter and simultaneously measure a pair of orthogonal field quadratures at the outputs using tomographic `Q-function homodyne detection' (QHD). The final act is probabilistic two-copy data post-processing aiming for data from a new state with larger photon number. Evaluating the final tomographic data as that of a grown microscopic Schr{\"o}dinger cat state shows that the probabilistic post-processing increased the photon number of $|\alpha_0|^2 \approx 1.2$ to $|\alpha_2|^2 \approx 6.8$. Our concept for obtaining tomographic measurement data of mesoscopic non-classical states that never existed might be a turning point in measurement-based quantum technology.