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In quantum Shannon theory, transmission of information is enhanced by quantumfeatures. Up to very recently, the trajectories of transmission remained fullyclassical. Recently, a new paradigm was proposed by playing quantum tricks ontwo completely depolarizing quantum channels i.e. using coherent control inspace or time of the two quantum channels. We extend here this control to thetransmission of information through a network of an arbitrary number $N$ ofchannels with arbitrary individual capacity i.e. information preservationcharacteristics in the case of indefinite causal order. We propose a formalismto assess information transmission in the most general case of $N$ channels inan indefinite causal order scenario yielding the output of such transmission.Then we explicitly derive the quantum switch output and the associated Holevolimit of the information transmission for $N=2$, $N=3$ as a function of allinvolved parameters. We find in the case $N=3$ that the transmission ofinformation for three channels is twice of transmission of the two channel casewhen a full superposition of all possible causal orders is used.

Communication Enhancement Through Quantum Coherent Control of $N$ Channels in an Indefinite Causal-order Scenario