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- Aerts, D. and Daubechies, I. (1978). About the structure-preserving maps of a quantum mechanical propositional system.
Helvetica Physica Acta,51,pp. 637-660. doi: 10.5169/seals-114964. download pdf.

Abstract:We study c-morphisms from one Hilbert space lattice (with dimension at least three) to another one; we show that for a c-morphism conserving modular pairs, there exists a linear structure underlying such a morphism, which enables us to construct explicitly a family of linear maps generating this morphism. As a special case we prove that a unitary c-morphism which preserves the atoms (i.e. maps one- dimensional subspaces into one-dimensional subspaces) is necessarily an isomorphism. Counterexamples are given when the Hilbert space has dimension 2.- Aerts, D. and Daubechies, I. (1978). Physical justification for using the tensor product to describe two quantum systems as one joint system.
Helvetica Physica Acta,51,pp. 661-675. doi:10.5169/seals-114965. download pdf.

Abstract:We require the following three conditions to hold on two systems being described as a joint system: (1) the structure of the two systems is preserved: (2) a measurement on one of the systems does not disturb the other one; (3) maximal information obtained on both systems separately gives maximal information on the joint system. With these conditions we show, within the framework of the propositional system formalism, that if the systems are classical the joint system is described by the cartesian product of the corresponding phase spaces, and if the systems are quantal the joint system is described by the tensor product of the corresponding Hilbert spaces.

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1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000,