Skip to main content
Geometry of Quantum States
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 505
  • Cited by
    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Adamczak, Radosław Latała, Rafał Puchała, Zbigniew and Życzkowski, Karol 2017. Asymptotic entropic uncertainty relations. Journal of Mathematical Physics, Vol. 57, Issue. 3, p. 032204.

    Aniello, Paolo and Chruściński, Dariusz 2017. Characterizing the dynamical semigroups that do not decrease a quantum entropy. Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue. 34, p. 345301.

    Aubourg, Lucile and Viennot, David 2017. Information transmission and control in a chaotically kicked spin chain. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 49, Issue. 11, p. 115501.

    Augusiak, R. Kołodyński, J. Streltsov, A. Bera, M. N. Acín, A. and Lewenstein, M. 2017. Asymptotic role of entanglement in quantum metrology. Physical Review A, Vol. 94, Issue. 1,

    Balz, Ben N. and Reimann, Peter 2017. Equilibration of isolated many-body quantum systems with respect to general distinguishability measures. Physical Review E, Vol. 93, Issue. 6,

    Bastos, Catarina Bernardini, Alex E. Bertolami, Orfeu Dias, Nuno Costa and Prata, João Nuno 2017. Bell operator and Gaussian squeezed states in noncommutative quantum mechanics. Physical Review D, Vol. 93, Issue. 10,

    Bosyk, G. M. Zozor, S. Holik, F. Portesi, M. and Lamberti, P. W. 2017. A family of generalized quantum entropies: definition and properties. Quantum Information Processing, Vol. 15, Issue. 8, p. 3393.

    Carmeli, Claudio Heinosaari, Teiko Karlsson, Antti Schultz, Jussi and Toigo, Alessandro 2017. Verifying the Quantumness of Bipartite Correlations. Physical Review Letters, Vol. 116, Issue. 23,

    Chakraborty, Romit and Mazziotti, David A. 2017. Role of the generalized pauli constraints in the quantum chemistry of excited states. International Journal of Quantum Chemistry, Vol. 116, Issue. 10, p. 784.

    Collins, Benoît and Nechita, Ion 2017. Random matrix techniques in quantum information theory. Journal of Mathematical Physics, Vol. 57, Issue. 1, p. 015215.

    Contreras, I. Ercolessi, E. and Schiavina, M. 2017. On the geometry of mixed states and the Fisher information tensor. Journal of Mathematical Physics, Vol. 57, Issue. 6, p. 062209.

    Czerwiński, Artur 2017. Applications of the Stroboscopic Tomography to Selected 2-Level Decoherence Models. International Journal of Theoretical Physics, Vol. 55, Issue. 2, p. 658.

    Dehdashti, Shahram Mahdifar, Ali and Wang, Huaping 2017. Coherent States of Position-Dependent Mass Oscillator. International Journal of Theoretical Physics, Vol. 55, Issue. 8, p. 3564.

    Deschamps, Julien Nechita, Ion and Pellegrini, Clément 2017. On some classes of bipartite unitary operators. Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue. 33, p. 335301.

    Dive, Benjamin Burgarth, Daniel and Mintert, Florian 2017. Isotropy and control of dissipative quantum dynamics. Physical Review A, Vol. 94, Issue. 1,

    Duan, Xie and Haifeng, Chen 2017. Quantum noise on the coherent-transport protocol for clock synchronization. Journal of the Korean Physical Society, Vol. 68, Issue. 4, p. 497.

    Enríquez, M Wintrowicz, I and Życzkowski, K 2017. Maximally Entangled Multipartite States: A Brief Survey. Journal of Physics: Conference Series, Vol. 698, p. 012003.

    Faist, Philippe and Renner, Renato 2017. Practical and Reliable Error Bars in Quantum Tomography. Physical Review Letters, Vol. 117, Issue. 1,

    Frey, Michael R. 2017. Quantum speed limits—primer, perspectives, and potential future directions. Quantum Information Processing,

    Gong, Zongping Ashida, Yuto and Ueda, Masahito 2017. Quantum-trajectory thermodynamics with discrete feedback control. Physical Review A, Vol. 94, Issue. 1,

  • Export citation
  • Recommend to librarian
  • Recommend this book

    Email your librarian or administrator to recommend adding this book to your organisation's collection.

    Geometry of Quantum States
    • Online ISBN: 9780511535048
    • Book DOI:
    Please enter your name
    Please enter a valid email address
    Who would you like to send this to? *
  • Buy the print book

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

    • Aa
    • Aa
Refine List
Actions for selected content:
Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Send to Kindle
  • Send to Dropbox
  • Send to Google Drive
  • Send content to

    To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to .

    To send content to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

    Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

    Find out more about the Kindle Personal Document Service.

    Please be advised that item(s) you selected are not available.
    You are about to send:

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.


Full text views

Total number of HTML views: 0
Total number of PDF views: 1602 *
Loading metrics...

Book summary page views

Total views: 740 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd September 2017. This data will be updated every 24 hours.