Entanglement of mixed quantum states for qubits and qudit in double photoionization of atoms

Quantum entanglement and its paradoxical properties are genuine physical resources for various quantum information tasks like quantum teleportation, quantum cryptography, and quantum computer technology. The physical characteristic of the entanglement of quantum-mechanical states, both for pure and mixed, has been recognized as a central resource in various aspects of quantum information processing. In this article, we study the bipartite entanglement of one electronic qubit along with the ionic qudit and also entanglement between two electronic qubits. The tripartite entanglement properties also have been investigated between two electronic qubits and an ionic qudit. All these studies have been done for the single-step double photoionization from an atom following the absorption of a single photon without observing spin orbit interaction. The dimension of the Hilbert space of the qudit depends upon the electronic state of the residual photoion A2+. In absence of SOI, when Russell-Saunders coupling (L-S coupling) is applicable, dimension of the qudit is equal to the spin multiplicity of A2+. For estimations of entanglement and mixedness, we consider the Peres-Horodecki condition, concurrence, entanglement of formation, negativity, linear and von Neumann entropies. In case of L-S coupling, all the properties of a qubit-qudit system can be predicted merely with the knowledge of the spins of the target atom and the residual photoion.