a ) p. 131 The discussion between eqs. (5.14) and (5.15) is incorrect (dA should be made as large as possible!). b ) p. 256 In the figure, the numbers 6) and 7) occur twice. c ) p. 292 At the end of section 12.5, it should be the space of isospectral 0Hermitian matrices. d ) p. 306 A ”Tr” is missing in eq. (13.43). e ) p. 327, Eq. (14.64b) is 〈Trρ〉B = N(14N+10) (5N+1)(N+3) should be 〈Trρ〉B = 8N+7 (N+2)(N+4)

Geometry of Quantum States: Frontmatter

https://chaos.if.uj.edu.pl/~karol/erratum10.pdf

Geometry of Quantum States

Operators on Hilbert Space.- C*-Algebras.- Von Neumann Algebras.- Further Structure.- K-Theory and Finiteness.

Operator Algebras: Theory of C*-Algebras and von Neumann Algebras

Geometry of quantum states: an introduction to quantum entanglement by Ingemar Bengtsson and Karol Zyczkowski

Introduction- 1 Generalities for positive maps- 2 Jordan algebras and projection maps- 3 Extremal positive maps- 4 Choi matrices and dual functionals- 5 Mapping cones- 6 Dual cones- 7 States and positive maps- 8 Norms of positive maps- Appendix: A1 Topologies on B(H)- A2 Tensor products- A3 An extension theorem- Bibliography- Index 

/pdf/positive-linear-maps-of-operator-algebras-2va0ndd6xs.pdf

Positive Linear Maps of Operator Algebras

On the geometry of positive maps in matrix algebras

On the geometry of positive maps in matrix algebras. II

On the difference of n-positivity and complete positivity in C∗-algebras

Recent development of the theory of completely bounded maps between C*-algebras such as those results by Wittstock, Smith, Paulsen and Huruya are reviewed and discussed as well as the author's results. In recent development of the theory of operator algebras it has been recognized that particularity of infinite dimensional noncommutative order structure is in their matricial order and appropriate positivity of linear maps compatible with this order structure should be complete positivity. Thus as counterparts of completely positive maps we have to be naturally concerned with completely bounded maps when we consider bounded linear maps on operator algebras closely related to their structure. Recent results such as Christensen [5] and Haagerup [6] give evidence of this fact in the sense that solutions of the problems are equivalent to complete boundedness of involved maps. In this paper we intend to review recent development of the basic theory of completely bounded maps on C*-algebras. We shall be however mainly concerned with the results for the class of all completely bounded maps. In Section 2 we describe the solution on a pair of C*-algebras between which every bounded map becomes completely bounded. Results in this section also mean that in most cases the subspace of completely bounded maps is quite thin in the whole space of bounded linear maps. We shall deal with the growth of the norms of multiplicity maps in Section 3, determining the case where the norms of nmultiplicity map rn always coincides with the completely bounded norm \\t\\cb. In this section Theorem 3.2 and Proposition 3.4 seem to be new. Section 4 is Received January 5, 1983. * Faculty of Science, Niigata University, Niigata 950-21, Japan.

https://www.ems-ph.org/journals/show_pdf.php?issn=0034-5318&vol=19&iss=3&rank=17

Recent Development of the Theory of Completely Bounded Maps between C*-Algebras

/pdf/completely-positive-maps-in-the-tensor-products-of-von-3ym1edd6ko.pdf

Jun Tomiyama

Papers

On the geometry of positive maps in matrix algebras

On the geometry of positive maps in matrix algebras. II

On the difference of n-positivity and complete positivity in C∗-algebras

Recent Development of the Theory of Completely Bounded Maps between C*-Algebras

Completely positive maps in the tensor products of von Neumann algebras