Ueda, Y. (2018). On tensors of factorizable quantum channels with the completely depolarizing channel. Advances in Operator Theory, (), 1-9. doi: 10.15352/aot.1803-1340
Yuki Ueda. "On tensors of factorizable quantum channels with the completely depolarizing channel". Advances in Operator Theory, , , 2018, 1-9. doi: 10.15352/aot.1803-1340
Ueda, Y. (2018). 'On tensors of factorizable quantum channels with the completely depolarizing channel', Advances in Operator Theory, (), pp. 1-9. doi: 10.15352/aot.1803-1340
Ueda, Y. On tensors of factorizable quantum channels with the completely depolarizing channel. Advances in Operator Theory, 2018; (): 1-9. doi: 10.15352/aot.1803-1340
On tensors of factorizable quantum channels with the completely depolarizing channel
Department of Mathematics Hokkaido University, Japan
Receive Date: 29 March 2018,
Revise Date: 21 May 2018,
Accept Date: 24 May 2018
Abstract
In this paper, we obtain results for factorizability of quantum channels. Firstly, we prove that if a tensor $T\otimes S_k$ of a quantum channel $T$ on $M_n(\mathbb{C})$ with the completely depolarizing channel $S_k$ is written as a convex combination of automorphisms on the matrix algebra $M_n(\mathbb{C})\otimes M_k(\mathbb{C})$ with rational coefficients, then the quantum channel $T$ has an exact factorization through some matrix algebra with the normalized trace. Next, we prove that if a quantum channel has an exact factorization through a finite dimensional von Neumann algebra with a convex combination of normal faithful tracial states with rational coefficients, then it also has an exact factorization through some matrix algebra with the normalized trace.