Topological tenfold classification and the entanglement of two qubits

The authors reveal here a key link between quantum entanglement and the topology of Hilbert spaces in condensed matter physics. Antiunitary symmetries and the Cartan tenfold classification connect the entanglement of evolution operators with the topology of the Hamiltonian. The study is validated with two-qubit systems and establishes groundwork for expanding to complex systems. Direct mapping to quantum graphs enables computation of topological integers.