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arXiv · 2209.07504

Computing mixed Schatten norm of completely positive maps

Mohammad ShahverdiKondori·Sio On Chan
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Abstract

Computing $p \rightarrow q$ norm for matrices is a classical problem in computational mathematics and power iteration is a well-known method for computing $p \rightarrow q $ norm for a matrix with nonnegative entries. Here we define an equivalent iteration method for computing $ S_p \rightarrow 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.

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Mohammad ShahverdiKondori, Sio On Chan. 2022-09-15. Computing mixed Schatten norm of completely positive maps. https://arxiv.org/abs/2209.07504

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