  Chiral integer quantum Hall (QH) edge modes are immune to backscattering and
therefore are non-localized and show a vanishing longitudinal as well as
non-local resistance along with quantized 2-terminal and Hall resistance even
in the presence of sample disorder. However, this is not the case for contact
disorder, which refers to the possibility that a contact can reflect edge modes
either partially or fully. This paper shows that when all contacts are
disordered in a N-terminal quantum Hall bar, then transport via chiral QH edge
modes can have a significant localization correction. The Hall and 2-terminal
resistance in an N-terminal quantum Hall sample deviate from their values
derived while neglecting the phase acquired at disordered contacts, and this
deviation is called the quantum localization correction. This correction term
increases with the increase of disorderedness of contacts but decreases with
the increase in the number of contacts in an N-terminal Hall bar. The presence
of inelastic scattering, however, can completely destroy the quantum
localization correction.
