  It is proven that the logarithmic negativity does not increase on average
under positive partial transpose preserving (PPT) operation including
subselection (a set of operations that incorporate local operations and
classical communication (LOCC) as a subset) and, in the process, a further
proof is provided that the negativity does not increase on average under the
same set of operations. Given that the logarithmic negativity is obtained from
the negativity applying a concave function and is itself not a convex quantity
this result is surprising as convexity is generally considered as describing
the local physical process of losing information. The role of convexity and in
particular its relation (or lack thereof) to physical processes is discussed in
this context.

Quantum Physics