## Advances in Operator Theory

- Adv. Oper. Theory
- Volume 3, Number 4 (2018), 807-815.

### On tensors of factorizable quantum channels with the completely depolarizing channel

#### 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.

#### Article information

**Source**

Adv. Oper. Theory, Volume 3, Number 4 (2018), 807-815.

**Dates**

Received: 29 March 2018

Accepted: 24 May 2018

First available in Project Euclid: 8 June 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.aot/1528444824

**Digital Object Identifier**

doi:10.15352/aot.1803-1340

**Mathematical Reviews number (MathSciNet)**

MR3856174

**Zentralblatt MATH identifier**

06946379

**Subjects**

Primary: 46L07: Operator spaces and completely bounded maps [See also 47L25]

Secondary: 15A60 47C15 47L07

**Keywords**

Markov map factorizable quantum channel completely depolarizing channel

#### Citation

Ueda, Yuki. On tensors of factorizable quantum channels with the completely depolarizing channel. Adv. Oper. Theory 3 (2018), no. 4, 807--815. doi:10.15352/aot.1803-1340. https://projecteuclid.org/euclid.aot/1528444824