Bell's inequality is a necessary condition for the existence of a classical probabilistic model for a given set of correlation functions. This condition is not satisfied by the quantum-mechanical correlations of two-spin systems in a singlet state. We give necessary and sufficient conditions, on the transition probabilities, for the existence of a classical probabilistic model. We also give necessary and sufficient conditions for the xistence of a complex (respectively real) Hilbert space model. Our results apply to individual-spin systems hence they need no locality assumption. When applied to the quantum-mechanical transition probabilities, they prove not only the necessity of a nonclassical probabilistic model, but also the necessity of using complex ather than real Ililbert spaces.

On the Statistical Meaning of Complex Numbers in Quantum Mechanics

FEDULLO, Aniello
1982

Abstract

Bell's inequality is a necessary condition for the existence of a classical probabilistic model for a given set of correlation functions. This condition is not satisfied by the quantum-mechanical correlations of two-spin systems in a singlet state. We give necessary and sufficient conditions, on the transition probabilities, for the existence of a classical probabilistic model. We also give necessary and sufficient conditions for the xistence of a complex (respectively real) Hilbert space model. Our results apply to individual-spin systems hence they need no locality assumption. When applied to the quantum-mechanical transition probabilities, they prove not only the necessity of a nonclassical probabilistic model, but also the necessity of using complex ather than real Ililbert spaces.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/1551396
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