Quantum Synchronizing Words: Resetting and Preparing Qutrit States

TL;DR

This paper introduces a quantum analogue of synchronizing words, showing that two quantum channels can reset any qutrit state and prepare arbitrary states, with potential applications in universal quantum gate design.

Contribution

It extends classical automata synchronizing concepts to quantum systems, demonstrating reset and state preparation capabilities with minimal quantum channels.

Findings

Two quantum channels can reset any qutrit state.

The same channels can prepare arbitrary pure real qutrit states.

Potential for designing minimal universal quantum gates.

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 show that with only two quantum channels, it is possible to bring an arbitrary qutrit state close to a designated target state. Furthermore, we demonstrate that following this reset, any pure real qutrit state can be closely approximated using the same two channels. These findings establish a quantum analogue of synchronizing words, highlighting their potential applications in constructing minimal sets of universal quantum gates capable of both resetting and preparing arbitrary states.