  The concepts of Riesz type and cotype of a given Banach space are extended to
a non-commutative setting. First, the Banach space is replaced by an operator
space. The notion of quantized orthonormal system, which plays the role of the
orthonormal system in the classical setting, is then defined. The Fourier type
and cotype of an operator space with respect to a non-commutative compact group
fit in this context. Also, the quantized analogs of Rademacher and Gaussian
systems are treated. All this is used to obtain an operator space version of
the classical theorem of Kwapie\'n characterizing Hilbert spaces by means of
vector-valued orthogonal series. Several approaches to this result with
different consequences are given.
