Spectral decomposition of wide-sense stationary quantum random processes

Mario Castagnino, R. Id Betán, Roberto Laura

John Edward Gough

We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra. The power spectrum of such a process is defined, in analogy to classical theory, as a positive measure on frequency space taking values in the expected algebra. The notion of linear quantum filters is introduced as some simple examples mentioned.

Burkhard Kümmerer

Louis Sica

Correlations for the Bell gedankenexperiment are constructed using probabilities given by quantum mechanics, and nonlocal information.They satisfy Bell's inequality and exhibit spatial non stationarity in angle.Correlations for three successive local spin measurements on one particle are computed as well.These correlations also exhibit non stationarity, and satisfy the Bell inequality.In both cases, the mistaken assumption that the underlying process is wide-sense-stationary in angle results in violation of Bell's inequality.These results directly challenge the wide-spread belief that violation of Bell's inequality is a decisive test for nonlocality.

Mohamed Ben Chrouda, MOHAMED EL OUED, Habib Ouerdiane

Louis Sica

Correlations for the Bell gedankenexperiment are constructed using probabilities given by quantum mechanics, and non-local information. They satisfy Bell's inequality and exhibit spatial non-stationarity in angle. Correlations for three successive local spin measurements on one particle are computed as well. These correlations also exhibit non-stationarity, and satisfy the Bell inequality. In both cases, the mistaken assumption that the underlying process is wide-sense-stationary in angle results in violation of Bell's inequality. These results directly challenge the wide-spread belief that violation of Bell's inequality is a decisive test for non-locality.