  Continuous frames and tensor products are important topics in theoretical
physics. This paper combines those concepts. We derive fundamental properties
of continuous frames for tensor product of Hilbert spaces. This includes, for
example, the consistency property, i.e. preservation of the frame property
under the tensor product, and the description of the canonical dual tensors by
those on the Hilbert space level. We show the full characterization of all dual
systems for a given continuous frame, a result interesting by itself, and apply
this to dual tensor frames. Furthermore, we discuss the existence on non-simple
tensor product (dual) frames. Continuous frame multipliers and their Schatten
class properties are considered in the context of tensor products. In
particular, we give sufficient conditions for obtaining partial trace
multipliers of the same form, which is illustrated with examples related to
short-time Fourier transform and wavelet localization operators. As an
application, we offer an interpretation of a class of tensor product continuous
frame multipliers as density operators for bipartite quantum states, and show
how their structure can be restricted to the corresponding partial traces.
