Quantum convolutional channels and multiparameter families of 2-unitary matrices

Many alternative approaches to construct quantum channels with large entangling capacity were proposed in the past decade, resulting in multiple isolated gates. In this work, we put forward a novel one, inspired by convolution, which provides greater freedom of nonlocal parameters. Although quantum counterparts of convolution have been shown not to exist for pure states, several attempts with various degrees of rigorousness have been proposed for mixed states. In this work, we follow the approach based on coherifications of multi-stochastic operations and demonstrate a surprising connection to gates with high entangling power. In particular, we identify conditions necessary for the convolutional channels constructed using our method to possess maximal entangling power. Furthermore, we establish new, continuous classes of bipartite 2-unitary matrices of dimension <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>d</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>7</mml:mn> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>9</mml:mn> </mml:math> , with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>2</mml:mn> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>4</mml:mn> </mml:math> free nonlocal parameters beyond simple phasing of matrix elements, corresponding to perfect tensors of rank <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>4</mml:mn> </mml:math> or 4-partite absolutely maximally entangled states.