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Autumn 2018 On tensors of factorizable quantum channels with the completely depolarizing channel
Yuki Ueda
Adv. Oper. Theory 3(4): 807-815 (Autumn 2018). DOI: 10.15352/aot.1803-1340

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.

Citation

Download Citation

Yuki Ueda. "On tensors of factorizable quantum channels with the completely depolarizing channel." Adv. Oper. Theory 3 (4) 807 - 815, Autumn 2018. https://doi.org/10.15352/aot.1803-1340

Information

Received: 29 March 2018; Accepted: 24 May 2018; Published: Autumn 2018
First available in Project Euclid: 8 June 2018

zbMATH: 06946379
MathSciNet: MR3856174
Digital Object Identifier: 10.15352/aot.1803-1340

Subjects:
Primary: 46L07
Secondary: 15A60, 47C15, ‎47L07

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 4 • Autumn 2018
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