Multiplicativity of the maximal output 2-norm for depolarized Werner-Holevo channels

TL;DR

This paper proves that the output 2-norm multiplicativity holds for a specific class of depolarized Werner-Holevo channels, even though they do not satisfy certain positivity conditions, indicating a non-trivial result.

Contribution

It establishes the multiplicativity property for depolarized Werner-Holevo channels, expanding understanding beyond channels satisfying entrywise positivity conditions.

Findings

Multiplicativity holds for two identical depolarized Werner-Holevo channels.

Depolarized Werner-Holevo channels do not satisfy entrywise positivity.

Main result is non-trivial due to lack of entrywise positivity condition.

Abstract

We study the multiplicativity of the output 2-norm for depolarized Werner-Holevo channels and show that multiplicativity holds for a product of two identical channels in this class. Moreover, it shown that the depolarized Werner-Holevo channels do not satisfy the entrywise positivity condition introduced by C. King and M.B. Ruskai, which suggests that the main result is non-trivial.