The algebra of Grassmann canonical anti-commutation relations (GAR) and its applications to fermionic systems
Mathematical Physics
2014-11-20 v1 math.MP
Quantum Physics
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.
Keywords
Cite
@article{arxiv.0906.2929,
title = {The algebra of Grassmann canonical anti-commutation relations (GAR) and its applications to fermionic systems},
author = {Michael Keyl and Dirk-M. Schlingemann},
journal= {arXiv preprint arXiv:0906.2929},
year = {2014}
}
Comments
25 pages