  Quantum physics phenomena, entanglement and coherence, are crucial for
quantum information protocols, but understanding these in systems with more
than two parts is challenging due to increasing complexity. The W state, a
multipartite entangled state, is notable for its robustness and benefits in
quantum communication. Here, we generate an 8-mode on-demand single photon W
states, using nanowire quantum dots and a silicon nitride photonic chip. We
demonstrate a reliable, scalable technique for reconstructing W-state in
photonic circuits using Fourier and real-space imaging, supported by the
Gerchberg-Saxton phase retrieval algorithm. Additionally, we utilize an
entanglement witness to distinguish between mixed and entangled states, thereby
affirming the entangled nature of our generated state. The study provides a new
imaging approach of assessing multipartite entanglement in W-states, paving the
way for further progress in image processing and Fourier-space analysis
techniques for complex quantum systems.
