The unique and often-weird properties of quantum mechanics allow an information carrier to propagate through multiple trajectories of quantum channels simultaneously. This ultimately leads us to quantum trajectories with an indefinite causal order of quantum channels. It has been shown that indefinite causal order enables the violation of bottleneck capacity, which bounds the amount of the transferable classical and quantum information through a classical trajectory with a well-defined causal order of quantum channels. In this treatise, we investigate this beneficial property in the realm of both entanglement-assisted classical and quantum communications. To this aim, we derive closed-form capacity expressions of entanglement-assisted classical and quantum communication for arbitrary quantum Pauli channels over classical and quantum trajectories. We show that by exploiting the indefinite causal order of quantum channels, we obtain capacity gains over classical trajectory as well as the violation of bottleneck capacity for various practical scenarios. Furthermore, we determine the operating region where entanglement-assisted communication over quantum trajectory obtains capacity gain against classical trajectory and where the entanglement-assisted communication over quantum trajectory violates the bottleneck capacity.