Operational signatures of exceptional quantum channels

Abstract: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 $\Phi$, applied an integer number $n$ of times, while physical data are probabilities $p_n^{\mathbf A}(x|\rho)$ associated with states $\rho$ and observables $\mathbf A$ having measurements results $x$. We define exceptional channels through nontrivial Jordan chains of $\Phi$ 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.

arXiv:2610.13622 [quant-ph]

(or arXiv:2610.13622v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.13622 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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