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. |
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
1)/2 elements equal 2i fijk A₁ A2.4 Homomorphisms arbitrary bistochastic matrix Cartan subalgebra compatible affine connection component contravariant convex hull cos² covariant derivative covariant tensor CP¹ DBhatt defined dijk dimension distribution eigenvalues embedding entanglement equation exterior product fgeom Figure A3.2 fijk Ok fijm fmkn Fubini-Study 2-form geodesic glue Heegard decomposition Homomorphisms between low-dimensional Hopf circle hypersphere infinity integral intersection J₂ Lie algebra low-dimensional groups M¨obius strip manifold metric compatible affine Murray and Rice obtain one-forms Parallel transport partial trace Pauli matrices Pk Trpk plane points POVM Problem 2.2 qubits random pure representation Ricci tensor Riemann tensor Rijkl scalar products Schmidt decomposition sectional curvature sin² space of triplets spectrum SU(N subentropy tangent space tetrahedron theorem tori transformation transport of vectors Trpk In Pk Trpk ln unitary V₁ Wehrl entropy y₁ Życzkowski and Sommers μν Σ₁ σι σχ дхі ио
