Quantum Synchronization of Conjugated Variables in a Superconducting Device Leads to the Fundamental Resistance Quantization

We propose a way to achieve quantum synchronization of two canonically conjugated variables. For this, we employ a superconducting device where the synchronization of Josephson and Bloch oscillations results in the quantization of transresistance similar to that in the (fractional) quantum Hall effect. An LC oscillator is a key component to achieve an exponentially small rate of synchronization errors.