Bipartite depolarizing channels

22 06/2016

Wednesday, 22 Jun. 2016, 14:00 - 15:00

Presenter: Ludovico Lami
Host: Marcus Huber
Where: IQOQI Seminar Room, 2nd Floor, Boltzmanngasse 3, 1090 Vienna

Motivated by the study of a clear physical scenario, we introduce a 3–parameter class of maps acting on a bipartite quantum system that are a natural generalisation of the depolarizing channel (and include it as a special case). Then, we find the exact regions of the parameter space that alternatively determine a positive, completely positive, entanglement–breaking or entanglement–annihilating map. The model we propose displays a much richer behaviour than the one shown by a simple depolarizing channel, yet it stays exactly solvable. As an example of this richness, PPT but not entanglement–breaking maps are found, and a simple example of a positive yet indecomposable map is provided. The study of the entanglement–annihilating property is fully addressed and applied to solve the problem of the entanglement annihilation caused in a bipartite system by a tensor product of local depolarizing channels. In this context, a conjecture posed in [Filippov, JRL 2014] is affirmatively answered, and the gaps left open in [Filippov and Ziman, PRA 2013] are closed. To arrive at this result we employ a number of nontrivial techniques potentially useful in the study of the separability problem. Most notably, we point out and discuss properties of the Hadamard matrix product in quantum information.
Based on arXiv:1603.02158.