On tensors of factorizable quantum channels with the completely depolarizing channel

Yuki Ueda

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arXiv · 1803.10446

On tensors of factorizable quantum channels with the completely depolarizing channel

Yuki Ueda

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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.

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Yuki Ueda. 2018-03-28. On tensors of factorizable quantum channels with the completely depolarizing channel. https://arxiv.org/abs/1803.10446

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