  We present a new application of harmonic analysis to quantum information by
constructing intriguing classes of quantum channels stemming from specific
representations of multiplier algebras over locally compact groups $G$.
Beginning with a representation of the measure algebra $M(G)$, we unify and
elaborate on recent counter-examples to fixed point subalgebras in infinite
dimensions, as well as present an application to the noiseless subsystems
method of quantum error correction. Using a representation of the completely
bounded Fourier multiplier algebra $McbA(G)$, we provide a new class of
counter-examples to the recently solved asymptotic quantum Birkhoff conjecture,
along with a systematic method of producing the examples using a geometric
representation of Schur maps. Further properties of our channels including
duality, quantum capacity, and entanglement preservation are discussed along
with potential applications to additivity conjectures.
