Ueda, Y. (2018). On tensors of factorizable quantum channels with the completely depolarizing channel. Advances in Operator Theory, 3(4), 807-815. doi: 10.15352/aot.1803-1340

Yuki Ueda. "On tensors of factorizable quantum channels with the completely depolarizing channel". Advances in Operator Theory, 3, 4, 2018, 807-815. doi: 10.15352/aot.1803-1340

Ueda, Y. (2018). 'On tensors of factorizable quantum channels with the completely depolarizing channel', Advances in Operator Theory, 3(4), pp. 807-815. doi: 10.15352/aot.1803-1340

Ueda, Y. On tensors of factorizable quantum channels with the completely depolarizing channel. Advances in Operator Theory, 2018; 3(4): 807-815. 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.