Structure and Classification of Matrix Product Quantum Channels

• URL: http://arxiv.org/abs/2603.19866v1
• Date: Fri, 20 Mar 2026 11:34:36 GMT
• Title: Structure and Classification of Matrix Product Quantum Channels
• Abstract summary: We develop a framework for Matrix Product Quantum Channels (MPQCs)<n>We focus on translation-invariant channels, generated by a single repeated tensor, that admit a local purification.<n>We extend the framework to a broader class of translation-invariant channels capable of generating long-range entanglement.
• Score: 0.09999629695552194
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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