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The task is to show that even two copies of it cannot be processed into an entangled pair.","posed_since":"2022","precise":"Show that the $d = 4$ Werner state $\\rho(4, -1/2)$ is not 2-copy distillable: for all rank-2 projectors P, Q acting on two copies of each party's space, $\\left(P\\,\\operatorname{tensor}\\,Q\\right)\\left[(\\rho^\\Gamma)^{\\operatorname{tensor} 2}\\right]\\left(P\\,\\operatorname{tensor}\\,Q\\right)$ has no negative eigenvalue; or exhibit P, Q giving a negative eigenvalue. Its partial transpose is proportional to a unitary (Problem 5 of Horodecki, Rudnicki and Zyczkowski 2022).","problem_ref":null,"references":"","settled_by":"A proof of positivity over all rank-2 projector pairs, or explicit projectors giving a negative eigenvalue.","status_note":"","title":"Two-copy distillability of the two-ququart Werner state at $\\alpha = 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