Unbounded length minimal synchronizing words for quantum channels over qutrits
Bj{\o}rn Kjos-Hanssen, Swarnalakshmi Lakshmanan
TL;DR
This paper extends the construction of minimal synchronizing words for quantum channels over qutrits to arbitrary lengths, challenging classical automata conjectures and advancing quantum information theory.
Contribution
It introduces a method to create arbitrarily long minimal synchronizing words for qutrit quantum channels, expanding previous finite-length results.
Findings
Constructed quantum channels with arbitrarily long minimal synchronizing words
Contrasts with cernfdy's conjecture in automata theory
Provides new insights into quantum channel synchronization
Abstract
Grudka, Karczewski, Kurzynski, Stempin, W\'ojcik and Wojcik (2025) constructed quantum channels with synchronizing words of length 3 for qutrits. We extend their result to arbitrarily long minimal synchronizing words, providing a contrast to \v{C}ern\'y's conjecture for finite automata.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Mechanics and Applications · Quantum Information and Cryptography