Shaglel, SalwaSalwaShaglelImai, SatoyaSatoyaImai2026-07-062026-07-062026-06-02arXiv: 2606.03722 (2026)https://hdl.handle.net/11420/63683We develop systematic frameworks for characterizing the entanglement properties of two-qubit channels beyond unitary settings. We introduce averaged local-unitary invariants, referred to as moments, obtained from Haar integrals over input tates or unitaries. These moments provide computable descriptions of how a quantum channel can create, preserve, or destroy bipartite entanglement. We first show that second-order moments yield criteria for non-entangling and entanglementbreaking channels, which allow us to detect entanglement-creating and entanglement-preserving channels. We then demonstrate that higher-order moments can capture additional information and distinguish channels beyond second-order moments alone. Finally, we show that combinations of moments associated with different channel families improve the discrimination of locally inequivalent two-qubit unitaries.enhttps://creativecommons.org/licenses/by/4.0/Natural Sciences and Mathematics::530: PhysicsPreprint10.48550/arXiv.2606.0372210.15480/882.173762606.03722We thank Daniel Heineken, Martin Kliesch, Nikolai Miklin, and Stefan Nimmrichter for discussions. S.S. is funded by Fujitsu Germany GmbH and Dataport and the Hamburg Quantum Computing project, which is co-financed by the ERDF of the European Union and the Fonds of the Hamburg Ministry of Science, Research, Equalities and Districts (BWFGB). S.I. acknowledges support from JST ASPIRE (JPMJAP2339).