1202.3853 (Alexey E. Rastegin)

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

Alexey E. Rastegin

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 lower
bounds on norms of its partial trace in terms of the corresponding
dimensionality and norms of this operator. Similar inequalities, but in the
opposite direction, are obtained for certain anti-norms of positive matrices.
Applications of the results to generalized quantum entropies are discussed. We
derive inequalities between the unified entropies of a composite quantum system
and one of its subsystems, where the traced-out dimensionality is involved as
well.

View original: http://arxiv.org/abs/1202.3853