Detecting entanglement using a Path-entangled X-ray photon Probe

We develop a theoretical framework for using path-entangled X-ray NOON states as a novel probe of entanglement and correlations in quantum systems. Building on on-going experimental work of generating NOON states using synchrotron X-ray beams [1,2], as well as previous theoretical work on mode-entangled neutron probes [3], our approach leverages the interferometric sensitivity of NOON states to encode and reveal information about the target system’s correlations. We first present a phenomenological toy model where the entangled photons interact with a two-qubit system via controlled phase gates. This setup highlights key distinctions between using an entangled probe such as a NOON state and a classical probe like a coherent beam. We then extend the analysis to a microscopic scattering model based on the Jaynes–Cummings interaction, deriving how the NOON state scatters from the qubit pair and how the resulting interference encodes the system’s initial entanglement. This framework establishes a foundation for entanglement spectroscopy using quantum probes, opening pathways toward probing complex and strongly correlated systems such as quantum spin liquid candidate materials with entangled X-ray photons.

[1] S. M. Durbin, Journal of Applied Physics 131, 224401 (2022)

[2] L. T. Powers, M. Z. Kwasniewski, S. M. Durbin, AIP Advances 15,

045231 (2025)

[3] A. A. M. Irfan, P. Blackstone, R. Pynn, G. Ortiz, New Journal of

Physics 23, 083022 (2021)