Discrete reversible microcausality

This proof concerns observable operators, not superoperators. It also accounts for information transferred by interactions, rather than tracking only the relocation of one unchanged name.

For irreversible instruments, a local complete dilation or another localized observable representation must be specified. A channel adjoint is unital but generally not multiplicative. For example, a dephasing adjoint can send $X$ to $0$, while sending $X^2=I$ to $I$.