Another convex combination of product states for the separable Werner state (5 pages)

Shengjun Wu

Senlin Wu

Stanisław J. Szarek, Guillaume Aubrun

Hiroo Azuma, Masashi Ban

In this paper, we write down the separable Werner state in a two-qubit system explicitly as a convex combination of product states, which is different from the convex combination obtained by Wootters' method. The Werner state in a two-qubit system has a single real parameter and varies from inseparable to separable according to the value of its parameter. We derive a hidden variable model that is induced by our decomposed form for the separable Werner state. From our explicit form of the convex combination of product states, we understand the following: The critical point of the parameter for separability of the Werner state comes from positivity of local density operators of the qubits.

Razmik G. Unanyan, Hermann Kampermann, Dagmar Bruß

We derive an integral convex combination of product states for a range of separable Werner states. Our method consists of expanding the sought-after local density operators in terms of Wigner operators. For dimension d = 2, our decomposition holds for the whole separable range of Werner states, while for d > 2 it is valid for a subset of separable Werner states. We illustrate the general method with the explicit examples d = 2 and d = 3.

Dong-Ling Deng, Jing‐Ling Chen