Hamburg 2009 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 5: Quanteninformation: Konzepte I

Q 5.6: Vortrag

Montag, 2. März 2009, 12:00–12:15, VMP 6 HS-D

Analysis of fermionic gaussian states by non-commutative phase space techniques — •Dirk-Michael Schlingemann, Michael Keyl, and Lorenzo Campos Venuti — ISI Foundation Torino, Quantum information group

The basic constituents of the matter that surrounds us in daily life are fermions. Therefore it is needless to say that theoretical investigation of fermion systems play an essential role in almost all areas of quantum physics. A particular class of states of fermion systems are quasi-free states or Gaussian fermionic states. On one hand, this class of states can be treated analytically even for very large systems, on the other hand, these states are complex enough to describe ground states of interacting spin chain systems.

We present an approach to non-commutative phase space which allows to analyze Gaussian fermionic states in complete analogy to Gaussian bosonic states. The used mathematical tools are based on a novel algebraic structure which combines the Grassmann algebra with the fermion algebra of canonical anti-commutation relations (GAR algebra).

As a new application, the corresponding theory provides an elegant tool for calculating the fidelity of two fermionic gaussian states which is needed for the study of entanglement distillation within fermionic systems.