An unknown state of a quantum system S is usually determined by repeatedly measuring a set of non-commuting observables. The state can also be obtained from the repeated measurements of a single separable observable when the system S interacts with an assistant system A in a known state. In this paper, we study the quantum state tomography of a three-level atom （the system S） interacting with two radiation fields as the assistant system A. We obtain the initial state of S by repeatedly measuring a separable observable O = Sz n1 n2, in which Sz is the atom operator, and hi and h2 are the photon number operators of the two radiation fields. We achieve the one-to-one mapping M between the initial density matrix of the system S and the measured results of the single separable observable. We also give a concrete numerical example.
We propose a scheme for generating a hyperentangled four-photon cluster state that is simultaneously entangled in polarization modes and spatial modes. This scheme is based on linear optical elements, weak cross-Kerr nonlinearity, and homodyne detection. Therefore, it is feasible with current experimental technology.
In this paper, the entanglement dynamics of two two-level atoms trapped in coupled cavities with a Kerr medium is investigated, We find that the phenomena of entanglement sudden death （ESD） and entanglement sudden birth （ESB） appear during the evolution process. The influences of initial atomic states, Kerr medium, and cavity-cavity hopping rate on the atom-atom entanglement are discussed. The results obtained by the numerical method show that the atom- atom entanglement is strengthened and even prevented from ESD with increasing cavity-cavity hopping rate and Kerr nonlinearity.
