Heisenberg-Weyl basis observables and their application in entanglement detection

Seminar author:Claudio Kloeckl

Event date and time:02/25/2016 02:30:pm

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Bloch vectors provide a very useful geometrical representation of quantum states for characterizing their properties. We establish a new basis of observables constructed by a suitable combination of the non-Hermitian generalization of the Pauli matrices, the Heisenberg-Weyl operators. This allows us to identify a (Hermitian) Bloch representation for an arbitrary density operator of finite, as well as infinite dimensional systems in terms of complete set of Heisenberg-Weyl observables. Compared to the canonical basis of Generalized Gell-Mann operators, the Heisenberg-Weyl based observables exhibit a number of advantageous properties which we highlight in the context of entanglement detection.