A relation between completely bounded norms and conjugate channels

2006/01/11 by Anna Jencova, Anna Jenčová, Jencova, Anna · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #math.OA #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0601071

5 pages, we make a connection between quant-ph/0506196 and the papers quant-ph/0509101 and quant-ph/0509126

arxiv created 2006/01/11 · openalex publication_date 2006/01/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show a relation between a quantum channel Φ and its conjugate Φ^C, which implies that the p→ p Schatten norm of the channel is the same as the 1→ p completely bounded norm of the conjugate. This relation is used to give an alternative proof of the multiplicativity of both norms.

Cited by

• Completely Bounded Qusi-Norms, Their Mutiplicativity, and New Additivity Results of Quantum Channels
• Multiplicativity of Completely Bounded p-Norms Implies a Strong Converse for Entanglement-Assisted Capacity

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