Structure and Classification of Matrix Product Quantum Channels

Abstract:We develop a framework for Matrix Product Quantum Channels (MPQCs), a one-dimensional tensor-network description of completely positive, trace-preserving maps. We focus on translation-invariant channels, generated by a single repeated tensor, that admit a local purification. We show that their purifying isometry can always be implemented by a constant-depth brickwork quantum circuit, implying that such channels generate only short-range correlations when applied on product states. In contrast to the unitary setting, where one-dimensional quantum cellular automata (in one-to-one correspondence with matrix product unitaries) carry a nontrivial index, we prove that all locally purified channels belong to a single phase, that is, they can be continuously deformed into one another. We then extend the framework to a broader class of translation-invariant channels capable of generating long-range entanglement and show that these remain deterministically implementable in constant depth using two rounds of measurements and feedforward.

Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph)

arXiv:2603.19866 [quant-ph]

(or arXiv:2603.19866v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.19866 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. Lett. 137, 120401 (2026)

https://doi.org/10.1103/4216-bgrp Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.