Violation of the quantum regression theorem and the Leggett-Garg inequality in an exactly solvable model

Violation of the quantum regression theorem and the Leggett-Garg inequality is studied by means of the exactly solvable multi-mode Jaynes-Cummings model. An exact expression of a two-time correlation function is compared with that derived by the quantum regression theorem. It is found that the quantum regression theorem is not valid even if the reduced time evolution of the qubit is Markovian. Furthermore, it is shown that if the quantum regression theorem is applied in this model, the Leggett-Garg inequality is satisfied while it is violated by the exact correlation function.