## Advances in Operator Theory

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

Yuki Ueda

#### Advance publication

This article is in its final form and can be cited using the date of online publication and the DOI.

#### 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, Advance publication (2018), 13 pages.

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

Subjects
Primary: 46L07: Operator spaces and completely bounded maps [See also 47L25]
Secondary: 15A60‎ ‎47C15‎ ‎47L07

#### Citation

Ueda, Yuki. On tensors of factorizable quantum channels with the completely depolarizing channel. Adv. Oper. Theory, advance publication, 8 June 2018. doi:10.15352/aot.1803-1340. https://projecteuclid.org/euclid.aot/1528444824

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