Relations for certain symmetric norms and anti-norms before and after partial trace

Understand

Changes of some unitarily invariant norms and anti-norms under the operation of partial trace are examined.

• The norms considered form a two-parametric family, including both the Ky Fan and Schatten norms as particular cases.
• The obtained results concern operators acting on the tensor product of two finite-dimensional Hilbert spaces.
• For any such operator, we obtain upper bounds on norms of its partial trace in terms of the corresponding dimensionality and norms of this operator.