Amselem and Bourennane reply

The goal of our experiment was to prepare a quantum state as close as possible to the pure four-qubit bound entangled (BE) Smolin1 state ρS and show its entanglement properties.

To investigate the properties of the Smolin state ρS experimentally and fully, we have evaluated the four-photon 16 × 16 density matrix ρS by the quantum state tomography method. The separability across the bipartite AB|CD, AC|BD and AD|BC cuts was tested using the PPT criterion. Our results have shown that all the eigenvalues are positive or zero within experimental error, indicating separability across these cuts. To rule out one–three qubit separability and three-party entanglement, a stabilizer witness was constructed. We have also demonstrated the distillation protocol and violation of the Bell inequality2.

It is well known that noisy Smolin states of the form — a mixture of Smolin state and depolarizing noise, where p is the amount of noise, 0 ≤ p < 2/3 — are bound entangled states3. In recent experiments4,5, the search for bound entanglement was done by scanning over the family of these noisy Smolin states. Iterative quantum state tomography and Monte Carlo simulations over obtained data, and elaborated error analysis, were then used. Therefore these refinements show the bound entanglement more clearly.

After your comment, we have reanalysed our data and we have found that the errors on the eigenvalues of the partial transpose on the bipartite AB|CD, AC|BD and AD|BC cuts are correlated, thus giving less evidence for the separability criterion. By adding depolarizing noise to our experimental ρSexp, we have reinvestigated the entanglement properties of this noisy Smolin state. Our results give strong evidence for bound entanglement for an amount of depolarizing noise with 0.38 ≤ p < 0.58. The witness value for these states is negative and the eigenvalues of the partial transpose of all bipartite cuts are all positive. For example, for the less noisy state (p = 0.38), the lowest eigenvalue for the PPT criterion is 0.014 ± 0.009 and the witness value for three-party entanglement is −0.54 ± 0.01.