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Geometry of Quantum States
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  • Cited by 681
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Sohr, Philipp Link, Valentin Luoma, Kimmo and Strunz, Walter T 2019. Typical Gaussian quantum information. Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue. 3, p. 035301.

    Khvedelidze, Arsen Rogojin, Ilya Adam, Gh. Buša, J. Hnatič, M. and Podgainy, D. 2018. On the Generation of Random Ensembles of Qubits and Qutrits Computing Separability Probabilities for Fixed Rank States. EPJ Web of Conferences, Vol. 173, Issue. , p. 02010.

    Pezzè, Luca Smerzi, Augusto Oberthaler, Markus K. Schmied, Roman and Treutlein, Philipp 2018. Quantum metrology with nonclassical states of atomic ensembles. Reviews of Modern Physics, Vol. 90, Issue. 3,

    Heinosaari, Teiko Reitzner, Daniel Rybár, Tomáš and Ziman, Mário 2018. Incompatibility of unbiased qubit observables and Pauli channels. Physical Review A, Vol. 97, Issue. 2,

    Sauerwein, David Wallach, Nolan R. Gour, Gilad and Kraus, Barbara 2018. Transformations among Pure Multipartite Entangled States via Local Operations are Almost Never Possible. Physical Review X, Vol. 8, Issue. 3,

    Scharlau, Jakob and Mueller, Markus P. 2018. Quantum Horn's lemma, finite heat baths, and the third law of thermodynamics. Quantum, Vol. 2, Issue. , p. 54.

    Haase, J F Smirne, A Kołodyński, J Demkowicz-Dobrzański, R and Huelga, S F 2018. Fundamental limits to frequency estimation: a comprehensive microscopic perspective. New Journal of Physics, Vol. 20, Issue. 5, p. 053009.

    Debarba, Tiago 2018. Advanced Technologies of Quantum Key Distribution.

    Bueno, Pablo Cano, Pablo A. Hennigar, Robie A. and Mann, Robert B. 2018. NUTs and bolts beyond Lovelock. Journal of High Energy Physics, Vol. 2018, Issue. 10,

    Yang, Run-Qiu 2018. Complexity for quantum field theory states and applications to thermofield double states. Physical Review D, Vol. 97, Issue. 6,

    Manzano Paule, Gonzalo 2018. Thermodynamics and Synchronization in Open Quantum Systems. p. 257.

    Bhattacharyya, Arpan Takayanagi, Tadashi and Umemoto, Koji 2018. Entanglement of purification in free scalar field theories. Journal of High Energy Physics, Vol. 2018, Issue. 4,

    Aniello, Paolo 2018. A notion of symmetry witness related to Wigner’s theorem on symmetry transformations. Journal of Physics: Conference Series, Vol. 965, Issue. , p. 012004.

    Branford, Dominic Dahlsten, Oscar C. O. and Garner, Andrew J. P. 2018. On Defining the Hamiltonian Beyond Quantum Theory. Foundations of Physics, Vol. 48, Issue. 8, p. 982.

    Aurell, Erik 2018. Global Estimates of Errors in Quantum Computation by the Feynman–Vernon Formalism. Journal of Statistical Physics, Vol. 171, Issue. 5, p. 745.

    Takayanagi, Tadashi Ugajin, Tomonori and Umemoto, Koji 2018. Towards an entanglement measure for mixed states in CFTs based on relative entropy. Journal of High Energy Physics, Vol. 2018, Issue. 10,

    Bhatia, Rajendra Jain, Tanvi and Lim, Yongdo 2018. Strong convexity of sandwiched entropies and related optimization problems. Reviews in Mathematical Physics, Vol. 30, Issue. 09, p. 1850014.

    Faist, Philippe and Renner, Renato 2018. Fundamental Work Cost of Quantum Processes. Physical Review X, Vol. 8, Issue. 2,

    Portesi, M. Holik, F. Lamberti, P. W. Bosyk, G. M. Bellomo, G. and Zozor, S. 2018. Generalized entropies in quantum and classical statistical theories. The European Physical Journal Special Topics, Vol. 227, Issue. 3-4, p. 335.

    Di Martino, Sara Facchi, Paolo and Florio, Giuseppe 2018. Feynman graphs and the large dimensional limit of multipartite entanglement. Journal of Mathematical Physics, Vol. 59, Issue. 1, p. 012201.


Book description

Quantum 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.


'Geometry of Quantum States, not being a quantum mechanics textbook by itself, provides an extensive and detailed insight behind the scenes of entanglement and, as such, can serve as a very useful supplementary text for quantum mechanics courses. Written in a very lucid and engaging style, with numerous illustrations … The spectrum of potential readers … is by no means limited to students and newcomers. It is comprehensive enough to serve as a valuable reference for all researchers interested in quantum information theory. Geometry of Quantum States can be considered an indispensable item on a bookshelf of everyone interest in quantum information theory and its mathematical background.'

Milosz Michalski Source: Open Systems and Information Dynamics

'Bengtsson’s and Zyczkowski’s book is an artful presentation of the geometry that lies behind quantum theory … the authors collect, and artfully explain, many important results scattered throughout the literature on mathematical physics. The careful explication of statistical distinguishability metrics (Fubini-Study and Bures) is the best I have read.'

Gerard Milburn - University of Queensland

'Bengtsson and Zyczkowski's beautifully illustrated volume … attempts to cover considerable ground in its 418 pages.'

D. W. Hook Source: Journal of Physics

'The authors, distinguished mathematical physicists, have written a markedly distinctive, dedicatedly pedagogical, suitably rigorous text, designed, in part, for advanced undergraduates familiar with the principles of quantum mechanics. The book, pleasing in character and enthusiastic in tone, has many stimulating diagrams and tables, as well as problem sets (with hints and answers supplied at the end). The diverse topics covered - conveniently all assembled here - reflect the geometrically-oriented, fundamental quantum-information-theoretic interests and expertise of the two authors.'

Paul B. Slater Source: Mathematical Reviews

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