Operational signatures of exceptional quantum channels
Exceptional points (EPs) are usually introduced as defective degeneracies of non-Hermitian Hamiltonians and, in fully open quantum dynamics, of Liouvillian generators. Here we formulate an operational theory of exceptional points that does not invoke a Hamiltonian or a master equation. The primitive dynamical object is a completely positive trace-preserving (CPTP) quantum channel $Φ$, applied an integer number $n$ of times, while physical data are probabilities $p_n^{\mathbf A}(x|ρ)$ associated with states $ρ$ and observables $\mathbf A$ having measurements results $x$. We define exceptional channels through nontrivial Jordan chains of $Φ$ and show that a Jordan block of order $m$ generates discrete polynomial-exponential terms with maximal degree $m-1$. This places the physics of exceptional points in contact with what can be directly measured in experiments.