Convex combination of quantum states and characterization of correlation

Abstract In the study of optical quantum information, quantum teleportation can be realized by preparing multiphoton entangled states. Entanglement is a special quantum correlation, and there is also a quantum correlation in separable quantum States, which comes from the measurement of quantum states. Convex combinations of arbitrary quantum states are still quantum states. From the spectral decomposition of a quantum state, an ensemble formed by a complete eigenvector system can be determined, which corresponds to an orthogonal projection operator family with rank 1, and the convex combination of the operator family will correspond to a quantum state. The characterization of quantum correlation is an important issue in the study of quantum information theory. A Quantum state that remains unchanged under local orthogonal projection is a classical correlation state, which is not affected by decoherence. Based on the standard orthogonal basis, this paper considers the correlation of the quantum states formed by the convex combination of the operator family. According to the separability and entanglement of the ground state and the mutual dissimilarity of the corresponding non-zero eigenvalues, it is concluded that the convex combination of the operator family formed by the separable standard orthogonal basis in the composite system must be a classical correlation state. When the entangled pure state is an eigenvector, it is a quantum correlation state if the corresponding eigenvalue is a non-zero single value. In the case of multiple roots, we can illustrate that both are possible. For the correlation of unitary evolution of quantum states under different standard orthogonal bases, the evolution law is revealed by considering important quantum gates.