## States of quantum systems and their liftings

- Abstract: Let H_1 , H_2 be complex Hilbert spaces, H be their Hilbert tensor product and let tr_2 be the operator of taking the partial trace of trace class operators in H with respect to the space H_2 . The operation tr_2 maps states in H (i.e. positive trace class operators in H with trace equal to one) into states in H_1 . In this paper we give the full description of mappings that are linear right inverse to tr_2 . More precisely, we prove that any affine mapping F(W) of the convex set of states in H_1 into the states in H that is right inverse to tr_2 is given by W -> W x D for some state D in H_2 . In addition we investigate a representation of the quantum mechanical state space by probability measures on the set of pure states and a representation - used in the theory of stochastic Schrödinger equations - by probability measures on the Hilbert space. We prove that there are no affine mappings from the state space of quantum mechanics into these spaces of probability measures.

Author: | Joachim Kupsch |
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URN (permanent link): | urn:nbn:de:hbz:386-kluedo-11261 |

Document Type: | Preprint |

Language of publication: | English |

Year of Completion: | 2000 |

Year of Publication: | 2000 |

Publishing Institute: | Technische Universität Kaiserslautern |

Date of the Publication (Server): | 2001/04/05 |

Faculties / Organisational entities: | Fachbereich Physik |

DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |

Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |