  Filamentary resistive switching devices are not only considered as promising
building blocks for brain-inspired computing architectures, but they also
realize an unprecedented operation regime, where the active device volume
reaches truly atomic dimensions. Such atomic-sized resistive switching
filaments represent the quantum transport regime, where the transmission
eigenvalues of the conductance channels are considered as a specific device
fingerprint. Here, we gain insight into the quantum transmission properties of
close-to-atomic-sized resistive switching filaments formed across an insulating
Ta$_2$O$_5$ layer through superconducting subgap spectroscopy. This method
reveals the transmission density function of the open conduction channels
contributing to the device conductance. Our analysis confirms the formation of
truly atomic-sized filaments composed of 3-8 Ta atoms at their narrowest
cross-section. We find that this diameter remains unchanged upon resistive
switching. Instead, the switching is governed by the redistribution of oxygen
vacancies within the filamentary volume. The set/reset process results in the
reduction/formation of an extended barrier at the bottleneck of the filament
which enhances/reduces the transmission of the highly open conduction channels.
