New framework classifies Matrix Product Quantum Channels

Researchers at the Max-Planck-Institut für Quantenoptik are developing a framework for classifying Matrix Product Quantum Channels (MPQCs), a way to describe how quantum information changes in open systems. The authors state that locally purified MPQCs can be implemented with constant-depth brickwork quantum circuits, meaning these channels generate only short-range correlations when applied to product states. Unlike their unitary counterparts, the researchers prove all locally purified channels belong to a single phase and can be continuously deformed into one another. The framework also extends to channels generating long-range entanglement, remaining implementable in constant depth using measurements and feedforward. This implementation suggests that channels within this class produce only short-range correlations when acting on product states, a limitation not typically observed in systems generating entanglement through more complex means. The research builds upon established tensor-network methods, including matrix product states and density operators, which have become essential for analyzing one-dimensional quantum systems, and extends their application to the realm of quantum channels. These channels, described as one-dimensional tensor networks, represent completely positive, trace-preserving maps, fundamental operations in…