Fe b 20 09 Markov triplets on CCR - algebras
نویسنده
چکیده
The paper contains a detailed computation about the algebra of canonical commutation relation, the representation of the Weyl unitaries, the quasi-free states and their von Neumann entropy. The Markov triplet is defined by constant entropy increase. The Markov property of a quasi-free state is described by the representing block matrix. The proof is based on results on the statistical sufficiency in the non-commutative case. The relation to classical Gaussian Markov triplets is also described. 2000 Mathematics Subject Classification. Primary 46L53, 60J10; Secondary 40C05, 81R15.
منابع مشابه
Markov property of Gaussian states of canonical commutation relation algebras
The Markov property of Gaussian states of CCR-algebras is studied. The detailed description is given by the representing block matrix. The proof is short and allows in nite dimension. The relation to classical Gaussian Markov triplets is also described. The minimizer of relative entropy with respect to a Gaussian Markov state has the Markov property. The appendix contains formulas for the relat...
متن کاملMarkov triplets on CCR-algebras
The paper contains a detailed computation about the algebra of canonical commutation relation, the representation of the Weyl unitaries, the quasi-free states and their von Neumann entropy. The Markov triplet is de ned by constant entropy increase. The Markov property of a quasi-free state is described by the representing block matrix. The proof is based on results on the statistical su ciency ...
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