Quantum dynamics is not strictly bidivisible
- URL: http://arxiv.org/abs/2203.13451v2
- Date: Thu, 8 Sep 2022 04:48:37 GMT
- Title: Quantum dynamics is not strictly bidivisible
- Authors: David Davalos, Mario Ziman
- Abstract summary: We show that for the qubit, those channels textitdo not exist, whereas for general finite-dimensional quantum channels the same holds at least for full Kraus rank channels.
We introduce a novel decomposition of quantum channels which separates them in a boundary and Markovian part, and it holds for any finite dimension.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 $n$ but not in $n+1$ parts. We show that for the qubit, those
channels \textit{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 in 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.
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