The measurement process in the generalized contexts formalism for quantum histories

MARCELO LOSADA

Ciudad de Buenos Aires

Jornada; V Jornadas de Fundamentos de Cuántica: problemas ontológicos a 80 años de EPR.; 2015

Universidad Nacional de La Plata

The quantum histories approach was developed in order to give an interpretation of quantum mechanics in which there is no collapse postulate and the measurement is considered as a quantum interaction between the measured system and the measurement instrument. Our formalism of Generalized Contexts is one of these formalisms of quantum histories, which allows to define expressions with properties at different times and enables to organize them in a valid quantum history.In this talk we applied this formalism to two consecutive non-ideal measurements on the same system. The measured system S and both measurement instruments A and B form a composed quantum system with a valid description, involving the possible pointer values of the instruments immediately after each of the two successive measurements. We proved that the possible values of the pointer variables, corresponding to two consecutive measurements on a system S are always compatible properties. Therefore, it is possible to use the formalism of Generalized Contexts to compute the probability for each result of the second measurement with instrument B, conditional to a given previous result of the firs measurement with instrument A. We proved that the value of this conditional probability is the same that would be obtained performing only a measurement with instrument B on the system S in an effective state. This effective state depends on the result of the first measurement. Only in the case of an ideal measurement the effective state coincides with the state obtained applying the state collapse postulate.