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Recently, a computational criterion of separability induced by the
greatest cross norm was proposed by Rudolph (2002 Preprint
quant-ph/0202121). There, Rudolph conjectured that the new
criterion is neither weaker nor stronger than the positive
partial-transpose criterion for separability. We show that there
exists a counterexample to the this claim, that is, the proposed
criterion is not equivalent to the positive partial-transpose
criterion.
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