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This paper operationalizes exceptional points (EPs) in quantum dynamics by defining them through the repeated application of completely positive trace-preserving (CPTP) quantum channels, bypassing the need for explicit Hamiltonians or master equations. The core insight is that nontrivial Jordan chains of a CPTP channel directly correspond to polynomial-exponential terms in observable measurement probabilities, with the Jordan block order dictating the maximal polynomial degree. This formulation connects the abstract concept of EPs to directly measurable experimental quantities.
Quantum channels, not Hamiltonians, reveal exceptional points through their Jordan chain structure, directly linking experimental probabilities to polynomial-exponential dynamics.
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.