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arXiv · 0906.2929

The algebra of Grassmann canonical anti-commutation relations (GAR) and its applications to fermionic systems

Michael Keyl·Dirk-M. Schlingemann
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Abstract

We present an approach to a non-commutative-like phase space which allows to analyze quasi-free states on the CAR algebra in analogy to quasi-free states on the CCR algebra. The used mathematical tools are based on a new algebraic structure the "Grassmann algebra of canonical anti-commutation relations" (GAR algebra) which is given by the twisted tensor product of a Grassmann and a CAR algebra. As a new application, the corresponding theory provides an elegant tool for calculating the fidelity of two quasi-free fermionic states which is needed for the study of entanglement distillation within fermionic systems.

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Michael Keyl, Dirk-M. Schlingemann. 2009-06-16. The algebra of Grassmann canonical anti-commutation relations (GAR) and its applications to fermionic systems. https://doi.org/10.1063/1.3282845

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