More Is Not Necessarily Easier

In this brief comment, we consider the exact, deterministic, and nonasymptotic transformation of multiple copies of pure states under LOCC. It was conjectured in quant-ph/0103131 that, if $k$ copies of $|\psi\>$ can be transformed to $k$ copies of $|\phi\>$, the same holds for all $r \geq k$. We present counterexamples to the above conjecture.