Entangled edge states of corank one with positive partial transposes

Abstract

We construct a parameterized family ofn circle times nPPT (positive partial transpose) states of corank one for eachn >= 3. With a suitable choice of parameters, we show that they aren circle times nPPT entangled edge states of corank one for 3 <= n <= 1000. They violate the range criterion for separability in the most extreme way. Note that corank one is the smallest possible corank for such states. The corank of the partial transpose is given by 2n- 3, which is also the smallest possible corank for the partial transposes of PPT entangled edge states of corank one. They provide the first explicit examples of such states forn >= 4.