More Is Not Necessarily Easier

Abstract

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 $|ψ\>$ can be transformed to $k$ copies of $|ϕ\>$, the same holds for all $r \geq k$. We present counterexamples to the above conjecture.

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