Continuous frames in tensor product Hilbert spaces, localization operators and density operators

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