Pashaev, OktayPashaev, Oktay04.02. Department of Mathematics04. Faculty of Science01. Izmir Institute of Technology2023-04-192023-04-19202397830312169922194-1009https://doi.org/10.1007/978-3-031-21700-5_10https://hdl.handle.net/11147/134183rd International Conference on Mathematics and its Applications in Science and Engineering, ICMASE 2022 -- 4 July 2022 through 7 July 2022 -- 291239Geometric relations between separable and entangled two-qubit and two-qutrit quantum information states are studied. For two qubit states a relation between reduced density matrix and the concurrence allows us to characterize entanglement by double area of a parallelogram, expressed by determinant of the complex Hermitian inner product metric. We find similar relation in the case of generic two-qutrit state, where the concurrence is expressed by sum of all 2 × 2 minors of 3 × 3 complex matrix. We show that for maximally entangled two-retrit state this relation is just De Gua’s theorem or a three-dimensional analog of the Pythagorean theorem for triorthogonal tetrahedron areas. Generalizations of our results for arbitrary two-qudit states are discussed © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.eninfo:eu-repo/semantics/openAccessDe Gua’s theoremEntanglementGeneralized Pythagoras theoremQuantum informationQutrit statesGeometryQuantum opticsQubitsDe gua’s theoremEntanglementGeneralized pythagora theoremGeometric relationsInformation statePythagorasQuantum InformationQutrit stateQutritsTetrahedraQuantum entanglementConference Object2-s2.0-8515106068110.1007/978-3-031-21700-5_10