  Any single system whose space of states is given by a separable Hilbert space
is automatically equipped with infinitely many hidden tensor-like structures.
This includes all quantum mechanical systems as well as classical field
theories and classical signal analysis. Accordingly, systems as simple as a
single one-dimensional harmonic oscillator, an infinite potential well, or a
classical finite-amplitude signal of finite duration, can be decomposed into an
arbitrary number of subsystems. The resulting structure is rich enough to
enable quantum computation, violation of Bell's inequalities, and formulation
of universal quantum gates. Less standard quantum applications involve a
distinction between position and hidden position. The hidden position can be
accompanied by a hidden spin, even if the particle is spinless. Hidden degrees
of freedom are in many respects analogous to modular variables. Moreover, it is
shown that these hidden structures are at the roots of some well known
theoretical constructions, such as the Brandt-Greenberg multi-boson
representation of creation-annihilation operators, intensively investigated in
the context of higher-order or fractional-order squeezing. In the context of
classical signal analysis, the discussed structures explain why it is possible
to emulate a quantum computer by classical analog circuit devices.
