:Geometry of Quantum States

The text begins by introducing the idea of convex sets, using color theory. It then discusses classical probability theory from a geometric perspective and develops the concept of complex projective space, after which it outlines the mathematical fundamentals of quantum mechanics. The following chapters then go into detail about topics within quantum theory, including coherent states, density matrices, aspects of quantum channels, distinguishability measures for quantum states, and von Neumann entropy.

The second edition added a chapter about discrete structures in finite-dimensional Hilbert spaces. This chapter covers topics related to mutually unbiased bases and the special quantum measurements known as SIC-POVMs.{{cite arXiv|first1=Ingemar |last1=Bengtsson |first2=Karol |last2=Życzkowski |author-link2=Karol Życzkowski |title=On discrete structures in finite Hilbert spaces |date=2017-01-26 |class=quant-ph |eprint=1701.07902}}

The text received generally positive reviews. Miłosz Michalski called the first edition "indispensable" for readers interested in the mathematics of quantum information, praising its writing style, use of illustrations, choice of exercises, and extensive collection of references.{{cite journal |last=Michalski |first=Miłosz |date=March 2008 |title=none |journal=Open Systems & Information Dynamics |language=en |volume=15 |issue=1 |pages=91–92 |doi=10.1142/S1230161208000080 |issn=1230-1612}} D. W. Hook also appreciated the illustrations, and singled out the authors' treatment of quantum measurements as particularly clear. Hook found the volume to be less a textbook and more a collection of largely self-contained essays.{{cite journal |last=Hook |first=D. W. |date=2008-01-11 |title=none |journal=Journal of Physics A: Mathematical and Theoretical |volume=41 |issue=1 |pages=019001 |doi=10.1088/1751-8121/41/1/019001 |issn=1751-8113}} Reviewing the book for MathSciNet, Paul B. Slater found it "a markedly distinctive, dedicatedly pedagogical, suitably rigorous text".{{cite arXiv |eprint=0901.4047 |first=Paul B. |last=Slater |title=Book Review: "Geometry of Quantum States" by Ingemar Bengtsson and Karol Zyczkowski (Cambridge University Press, 2006) |date=2009-01-26|class=math.HO }}

Gerard J. Milburn called the book "a delight to read and to savour". Its explanation of the Fubini–Study and Bures metrics were the best that he had encountered to date. Milburn opined that readers who wanted a quick introduction to

entanglement would benefit more from a shorter book, but those with the time to devote to the topic should "hang a gone fishin' notice on your office door" and read Bengtsson and Życzkowski.{{cite journal |last=Milburn |first=Gerard J. |year=2008 |title=Book review |url=https://www.rintonpress.com/journals/qic/8-89-860-860.pdf |journal=Quantum Information and Computation |volume=8 |page=0860 |number=8&9|doi=10.26421/QIC8.8-9-12 }}

• {{cite book |first1=Ingemar |last1=Bengtsson |first2=Karol |last2=Życzkowski |author-link2=Karol Życzkowski |title=Geometry of Quantum States: An Introduction to Quantum Entanglement |edition=1st |publisher=Cambridge University Press |year=2006 |isbn=978-0-521-81451-5 |mr=2230995}}
• {{cite book|first1=Ingemar |last1=Bengtsson |first2=Karol |last2=Życzkowski |title=Geometry of Quantum States: An Introduction to Quantum Entanglement |edition=2nd |publisher=Cambridge University Press |year=2017 |isbn=978-1-107-02625-4}}

{{Reflist}}

• Mathematical formulation of quantum mechanics

• [https://chaos.if.uj.edu.pl/~karol/geometry.htm Życzkowski's website with errata]

Category:2006 non-fiction books

Category:2017 non-fiction books

Category:Physics textbooks

Category:Quantum information science