Structure and Classification of Matrix Product Quantum Channels

Giorgio Stucchi; J. Ignacio Cirac; Rahul Trivedi; Georgios Styliaris

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arXiv · 2603.19866

Structure and Classification of Matrix Product Quantum Channels

Giorgio Stucchi·J. Ignacio Cirac·Rahul Trivedi·Georgios Styliaris

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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. 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.

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Giorgio Stucchi, J. Ignacio Cirac, Rahul Trivedi, Georgios Styliaris. 2026-03-20. Structure and Classification of Matrix Product Quantum Channels. https://arxiv.org/abs/2603.19866

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