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 Φ, applied an integer number n of times, while physical data are probabilities pnA(x|ρ) associated with states ρ and observables 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.
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BibTeX
@misc{brandao2026operational,
title = {{Operational signatures of exceptional quantum channels}},
author = {Paulo A. Brandão},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13622},
eprint = {2610.13622},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13622},
}
RIS
TY - UNPB
TI - Operational signatures of exceptional quantum channels
AU - Paulo A. Brandão
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13622
UR - https://arxiv.org/abs/2610.13622
AB - 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^A(x|ρ) associated with states ρ and observables 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.
ER -