  Exceptional bound (EB) states represent an unique new class of robust bound
states protected by the defectiveness of non-Hermitian exceptional points.
Conceptually distinct from the more well-known topological states and
non-Hermitian skin states, they were recently discovered as a novel source of
negative entanglement entropy in the quantum entanglement context. Yet, EB
states have been physically elusive, being originally interpreted as negative
probability eigenstates of the propagator of non-Hermitian Fermi gases. In this
work, we show that EB states are in fact far more ubiquitous, also arising
robustly in broad classes of systems whether classical or quantum. This hinges
crucially on a newly-discovered spectral flow that rigorously justifies the EB
nature of small candidate lattice systems. As a highlight, we present their
first experimental realization through an electrical circuit, where they
manifest as prominent stable resonant voltage profiles. Our work brings a
hitherto elusive but fundamentally distinctive quantum phenomenon into the
realm of classical metamaterials, and provides a novel pathway for the
engineering of robust modes in otherwise sensitive systems.
