Computing mixed Schatten norm of completely positive maps

2022/09/15 by Mohammad ShahverdiKondori, ShahverdiKondori, Mohammad, Sio On Chan +1 · 1 citation
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2209.07504

openalex publication_date 2022/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Computing p → q norm for matrices is a classical problem in computational mathematics and power iteration is a well-known method for computing p → q norm for a matrix with nonnegative entries. Here we define an equivalent iteration method for computing S_p → S_q norm for completely positive maps where S_p is the Schatten p norm. We generalize almost all of the definitions, properties, lemmas, etc. in the matrix setting to completely positive maps and prove an important theorem in this setting.

Cited by

• Complexity of mixed Schatten norms of quantum maps

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