  The study of scattered polarized light has led to important advances in
distinct fields such as astronomy, atmospheric sciences and bio-imaging. In
random diffusing media, light disorientation and the scrambling of its
polarization state appear to always occur together. Their apparent
inseparability suggests a profound connection between optical transport and
depolarization. Here, we present experimental evidence of their equivalence and
quantify their relationship in colloidal suspensions of microscopic
constituents. In particular, a proportionality relation between optical
transport lengths and their depolarization counterparts is provided. This
equivalence imposes depolarization whenever light traverses random media and
holds for wide spectral ranges and scatterer concentrations. Our results
clarify the connection between microscopic processes and measurable
polarization signatures.
