Successive measurements in photonic systems via indirect measurements (2016)
The importance of measurements in the quantum theory is such that one of the postulates of quantum mechanics is concerned in the possible outcomes and their corresponding probabilities of success. This postulate tells that, after a measurement, a certain amount of information is returned and the system is left in a corresponding state. The collapse of the state after the measurement prevents to obtain more information of conjugate physical quantities. However, on the frame of indirect measurements, based on the use of a weak coupling between the target variable of interest, and the meter that displays the result of the measurement, it is possible to execute a measurement over a quantum state without collapsing it. In this work is discussed the process of successive measurements over the polarization quantum state of an entangled photon pair using the frame of indirect measurements, and the process of Spontaneous Parametric Down Conversion (SPDC) Type-II as a source of entangled photons. In order to achieve this, the polarization quantum state (target) and the transversal momentum of the biphoton system (meter) are prepared and well defined. The first and second measurement consist on a weak coupling between the mentioned target and the meter, and a projection of the polarization state, respectively. The first measurement is performed and the possible results of the second measurement are discussed. It is shown that the result of the second measurement is closely related to the magnitude of the coupling performed in the first measurement, and that two successive measurement over different polarization basis can be performed, using the frame of indirect measurements with weak couplings(weak measurements). The result of non-collapsing measurements over quantum states can be of interest in the field of metrology and manipulation of quantum states, and the understanding of the results of this measurements may lead to interesting conclusions over fundamental physics.