Incoherent behavior of partially distinguishable photons (2502.05047v1)

Abstract: Photon distinguishability serves as a fundamental metric for assessing the quality of quantum interference in photocounting experiments. In the context of Boson Sampling, it plays a crucial role in determining classical simulability and the potential for quantum advantage. We develop a basis-independent framework for multi-photon interference, deriving a necessary and sufficient condition under which distinguishability manifests as stochastic errors. Additionally, we introduce an experimentally relevant operation, analogous to Pauli twirling, that enforces this condition. When satisfied, the condition allows any multi-photon state to be uniquely decomposed into a classical mixture of partition states -- discrete configurations representing different patterns of photon distinguishability. The resulting probability distribution over partition states defines the system's incoherent distinguishability spectrum, directly linking it to the complexity of classical simulation. This framework clarifies key challenges in defining genuine multi-photon indistinguishability, links previous perspectives on partial distinguishability, and provides a rigorous foundation for error mitigation and robust photonic operations.