Quantum Synchronizing Words

Abstract Synchronizing words in classical automata theory provide a mechanism to reset any state of a deterministic automaton to a specific target state via a carefully chosen finite sequence of transition rules. In this work, we extend the concept of synchronizing words to quantum information theory. Specifically, we investigate whether the concatenation of two non-resetting quantum channels can give rise to a resetting channel. While we formulate the problem for general qudits, the complexity of the setting leads us to focus on particular resetting concatenations for qubits and qutrits. Furthermore, we demonstrate that following the reset, any pure real qutrit state can be closely approximated using the same two non-resetting channels. These findings establish a quantum analogue of synchronizing words, highlighting their potential applications in constructing minimal sets of quantum channels capable of both resetting and preparing arbitrary states.