Bound entangled states with extremal properties

• Following recent work of Beigi and Shor, we investigate positive partial transpose (PPT) states that are heavily entangled. We first exploit volumetric methods to show that in a randomly chosen direction, there are PPT states whose distance in trace norm from separable states is (asymptotically) at least 1/4. We then provide explicit examples of PPT states which are nearly as far from separable ones as possible. To obtain a distance of 2 - c from the separable states, we need a dimension of 2(poly[log(1/epsilon)]), as opposed to 2(poly(1/epsilon)) given by the construction of Beigi and Shor [J. Math. Phys. 51, 042202 (2010)]. We do so by exploiting the so-called private states, introduced earlier in the context of quantum cryptography. We also provide a lower bound for the distance between private states and PPT states and investigate the distance between pure states and the set of PPT states.

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NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

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