## States, effects, and operations: fundamental notions of quantum theory : lectures in mathematical physics at the University of Texas at Austin |

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### Contents

1 States and Effects | 1 |

2 Operations | 13 |

3 The First Representation Theorem | 42 |

Copyright | |

4 other sections not shown

### Common terms and phrases

according adjoint analogous apparatus f applied arbitrary effects assume B(H 8 H Banach space Boolean algebra Borel sets coexistent effects complementary completely positive composite system condition 6.16 considered converges ultraweakly correlation effects corresponding decision effects defined definition density operators described effect apparatus effects F ensemble equivalence class f and g f e H F e L(H finite given H 8 H Hermitean Hilbert space implies index set interaction joint measurement Lemma linear mapping F ments Moreover n-positive non-selective operation numbers observable occur opera operators F operators on H orthogonal output channels pairs partial trace particle particular preparing instrument prestate probability projection operators quantum mechanics respectively right hand side satisfying scattering system selective operation self-adjoint operator single microsystem space H spectral subset subspaces suitable Theorem theory tion tr(FW tr(XT trace class triggered ultraweak uncorrelated vector f e yes-no measurements yields