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Many alternative approaches to construct quantum channels with largeentangling capacities were proposed in the past decade, resulting in multipleisolated gates. In this work, we put forward a novel one, inspired byconvolution, which provides greater freedom of nonlocal parameters. Althoughquantum counterparts of convolution have been shown not to exist for purestates, several attempts with various degrees of rigorousness have beenproposed for mixed states. In this work, we follow the approach based oncoherifications of multi-stochastic operations and demonstrate a surprisingconnection to gates with high entangling power. In particular, we identifyconditions necessary for the convolutional channels constructed using ourmethod to possess maximal entangling power. Furthermore, we establish new,continuous classes of bipartite 2-unitary matrices of dimension $d^2$ for $d =7$ and $d = 9$, with $2$ and $4$ free nonlocal parameters beyond simple phasingof matrix elements, corresponding to perfect tensors of rank $4$ or 4-partiteabsolutely maximally entangled states.

Quantum convolutional channels and multiparameter families of 2-unitary matrices