Complementary properties of multiphoton quantum states in linear optics networks

We have developed a theory for accessing quantum coherences in mutually unbiased bases associated with generalized Pauli operators in multiphoton multimode linear optics networks (LONs). We show a way to construct complementary Pauli measurements in multiphoton LONs and establish a theory for evaluation of their photonic measurement statistics without dealing with the computational complexity of Boson samplings. This theory extends characterization of complementary properties in single-photon LONs to multiphoton LONs employing convex-roof extension. It allows us to detect quantum properties such as entanglement using complementary Pauli measurements, which reveals the physical significance of entanglement between modes in bipartite multiphoton LONs.