 
Summary: Physical justification for using the tensor product
to describe two quantum systems as one joint
system
Diederik Aerts and Ingrid Daubechies
Theoretical Physics
Brussels Free University
Pleinlaan 2, 1050 Brussels, Belgium
diraerts@vub.ac.be, ingrid@math.princeton.edu
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 pre
served: (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.
1 Introduction
