Abstract
We address the question of the existence of quantum channels that are divisible in two quantum channels but not in three or, more generally, channels divisible in but not in parts. We show that for the qubit those channels do not exist, whereas for general finite-dimensional quantum channels the same holds at least for full Kraus rank channels. To prove these results, we introduce a novel decomposition of quantum channels which separates them into a boundary and Markovian part, and it holds for any finite dimension. Additionally, the introduced decomposition amounts to the well-known connection between divisibility classes and implementation types of quantum dynamical maps and can be used to implement quantum channels using smaller quantum registers.
- Received 28 March 2022
- Revised 8 September 2022
- Accepted 20 January 2023
DOI:https://doi.org/10.1103/PhysRevLett.130.080801
© 2023 American Physical Society