QuantumInfo.ClassicalInfo.Channel

Given a discrete memoryless channel $C$ with input alphabet $I$ and output alphabet $O$, and an input sequence $is \in I^n$ (modeled as a function $\text{Fin } n \to I$), the function returns the probability distribution over the output sequences $os \in O^n$ (functions $\text{Fin } n \to O$). The probability of receiving a specific output sequence $os$ given $is$ is defined as the product of the transition probabilities for each character: $$P(os \mid is) = \prod_{k=0}^{n-1} P_C(os_k \mid is_k)$$ where $P_C(o \mid i)$ is the probability provided by the channel $C$ for output $o$ given input $i$.

Given a discrete memoryless channel $C$ with input alphabet $I$ and output alphabet $O$, and a list of inputs $is = [i_0, i_1, \dots, i_{n-1}]$ of length $n$, this function defines a probability distribution over the sequences of outputs $(o_0, o_1, \dots, o_{n-1}) \in O^n$. The distribution is obtained by applying the channel $C$ independently to each element $i_k$ in the list.