Photon subtraction of thermal light with arbitrary beam splitting and imperfect photon-number-resolving detectors

We study feasible and effective techniques to improve the efficiency and fidelity of photon subtraction in order to enable practical quantum resource engineering based on it. We use thermal light for our investigation and consider non-negligible beam splitting beyond the conventional setup, also taking into account photon detection errors. We find that the output is still a photon-subtracted thermal state when a non-negligible amount of light is reflected from the input beam, but it has an effective mean photon number different than that of the input. It enables a strategy for achieving a target photon-subtracted thermal state by employing a stronger input light and leads to substantial improvement in the probability of successful photon subtraction events. We calculate the fidelity of the output state and analyze how it worsens with larger beam splitting ratios and photon counting errors. Using our understanding of the limiting factors in the conventional routine, we propose a new method for photon subtraction that can achieve high-fidelity output with decent efficiency, and using only mediocre photon detectors. We experimentally verify our solutions that are valuable for improving photon subtraction and lowering the experimental barrier.