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Entanglement witnesses for bipartite entanglement in 2N-qubit chains
Justyna P Zwolak
(Oregon State University)
Entanglement is considered to be the most nonclassi-
cal manifestation of quantum physics and is
fundamental to future quantum technologies. Character-
ization of entanglement (i.e., delineating entangled from
separable states) is equivalent to the characterization of positive, but not completely positive (PnCP), maps over matrix algebras.
For quantum states living in 2x2 and 2x3 dimensional
spaces there exists a complete characterization of separability problem (the celebrated Peres-Horodecki criterion). For increasingly higher dimensions this task becomes increasingly difficult. There is considerable effort devoted to constructing PnCP maps, but a
general procedure is still not known.
We are developing PnCP maps for higher dimensional systems. For instance, we recently generalized the Robertson map in a way that naturally meshes with 2N qubit systems, i.e., its structure respects the exponential growth of the state space. Using linear algebra techniques, we proved that this map is positive, but not completely positive, and also indecomposable and optimal. As such, it can be used to create witnesses that detect (bipartite) entanglement. We also determined the relation of our maps to entanglement breaking channels. As a byproduct, we provided a new example of a family of PPT (Positive Partial Transpose) entangled states. We will discuss this map as well as the new classes of entanglement witnesses.