## Geometry of Quantum States: An Introduction to Quantum EntanglementQuantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. After a gentle introduction to the necessary mathematics the authors describe the geometry of quantum state spaces. Focusing on finite dimensional Hilbert spaces, they discuss the statistical distance measures and entropies used in quantum theory. The final part of the book is devoted to quantum entanglement - a non-intuitive phenomenon discovered by Schrödinger, which has become a key resource for quantum computation. This richly-illustrated book is useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied. |

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### Contents

1 | |

Outline of quantum mechanics | 135 |

Coherent states and group actions | 156 |

The stellar representation | 182 |

The space of density matrices | 209 |

Puriﬁcation of mixed quantum states | 233 |

Quantum operations | 251 |

maps versus states | 281 |

Distinguishability measures | 323 |

Monotone metrics and measures | 339 |

Quantum entanglement | 363 |

1 | ix |

437 | |

440 | |

446 | |

452 | |

### Other editions - View all

Geometry of Quantum States: An Introduction to Quantum Entanglement Ingemar Bengtsson,Karol Życzkowski No preview available - 2006 |

Geometry of Quantum States: An Introduction to Quantum Entanglement Ingemar Bengtsson,Karol Zyczkowski No preview available - 2007 |

### Common terms and phrases

3-sphere acting algebra arbitrary ball base basis becomes Bloch bound bundle Bures called Chapter classical coherent complex compute condition cone consider consists convex coordinates corresponding curve deﬁned deﬁnition denote density matrices described diagonal dimension distance dynamical eigenvalues elements entanglement entropy equal equation exists fact Figure ﬁnd ﬁrst follows function geodesic geometry given gives Hence Hermitian Hilbert space interesting invariant known linear look manifold matrix maximal means measure mixed monotone namely natural normalized Note observe obtain operator orbit orthogonal phase plane points positive possible probability distribution Problem projective prove pure quantum mechanics random reference relation relative entropy representation represented respect result rotation sense separable simplex sphere tangent vector tensor theorem theory trace transformations unique unit unitary values vector zero