Pauli component erasing quantum channels

Decoherence of quantum systems is described by quantum channels. However, a complete understanding of such channels, especially in the multiparticle setting, is still an ongoing difficult task. We propose the family of quantum maps that preserve or completely erase the components of a multiqubit system in the basis of Pauli strings, which we call Pauli component erasing maps. For the corresponding channels, it is shown that the preserved components can be interpreted as a finite vector subspace, from which we derive several properties and complete the characterization. Moreover, we show that the obtained family of channels forms a semigroup and derive its generators. We use this simple structure to determine physical implementations and connect the obtained family of channels with Markovian processes.

Automated summary

This article proposes a method for translating quantum systems in a multiparticle environment, by preserving or erasing the components of a multiqubit system using the basis of Pauli strings. The preserved components are interpreted as a finite vector subspace, and the obtained family of channels is shown to form a semigroup with its generators determined. The physical implementations of the channels are also discussed and connected with Markovian processes.