John Watrous
Email: my last name at
Office: QNC 3312
Office hours: Tu 10–11, W 2:30–3:30

Teaching Assistant

Abel Molina
Email: amolinap at
Office: QNC 2212
Office hours: Th 4–5


Monday and Wednesday 10–11:20 in QNC 1201

Course information and materials

Course outline [pdf, html]

Course text:

J. Watrous. The Theory of Quantum Information. Cambridge University Press, 2018. [html]

Lecture schedule

The lectures topics listed below should be considered tentative for future lectures. Readings will be posted as the lectures take place.

September 4

Lecture 1: Course overview; registers and states

Reading: pages 58–64, plus the course outline

You may also wish to read through relevant parts of Chapter 1, to clarify the notation used in the course and to review various concepts from linear algebra. (In general, Chapter 1 should be consulted as needed, throughout the course.)

September 9

Lecture 2: Compound registers and reductions of states

Reading: pages 65–69.

September 11

Lecture 3: Purifications of states

Reading: pages 70–76. Also be sure to familiarize yourself with the operator-vector correspondence (i.e., the vec mapping) discussed on pages 23–24.

September 16

Lecture 4: Channels and their representations

Reading: pages 72–81.

September 18

Lecture 5: Characterizations of channels

Reading: pages 82–91.

September 23

Lecture 6: Examples of channels; measurements

Reading: pages 91–96, 100–109.

September 25

Lecture 7: Similarity and distance measures for states

Reading: pages 124–130. See also pages 31–34 concerning norms of operators.

September 30

Lecture 8: Fidelity

Reading: pages 139–163. (Note that we did not cover all of this material in the lecture, but we will come back to or make use of some of the additional material later in the course.)

October 2

Lecture 9: Optimal measurements and semidefinite programming (part 1)

Reading (for this lecture and the next): pages 53–57 and 132–136.

October 7

Lecture 10: Optimal measurements and semidefinite programming (part 2)

October 9

Lecture 11: Entropy and source coding

Reading: pages 283–293, plus the basic definitions on pages 250–252 and 265–266.

October 14

No lecture (Thanksgiving and reading week)

October 16

No lecture (Thanksgiving and reading week)

October 21

Lecture 12: Von Neumann entropy and quantum relative entropy

Reading: pages 250–274.

October 23

Lecture 13: Joint convexity of quantum relative entropy

Reading: pages 274–281.

October 28

Lecture 14: Strong subadditivity and Holevo's theorem

Reading: pages 281–282 and 294–300.

October 30

Lecture 15: Majorization for real vectors and Hermitian operators

Reading: pages 233–244.

November 4

Lecture 16: Weyl covariant channels and Schur channels

Reading: pages 212–222.

November 6

Lecture 17: Separability for states

Reading: pages 310–321.

November 11

Lecture 18: LOCC and separable channels

Reading: pages 322–332.

November 13

Lecture 19: Nielsen's theorem

Reading: pages 339–345.

November 18

Lecture 20: Measures of entanglement

Reading: pages 345–352.

November 20

Lecture 21: PPT states

Reading: pages 352–358.

November 25

Lecture 22: The completely bounded trace norm

Reading: pages 164–178 and 185–191.

November 27

Lecture 23: Unitarily invariant measures

Reading: pages 408–420. Pages 38–43 in Chapter 1 may also be helpful.

December 2

Lecture 24: Applications of unitarily invariant measures

Reading: pages 420–429.

Problem sets

Problem set 1

[pdf, LaTeX]

Problem set 2

[pdf, LaTeX]

Problem set 3

[pdf, LaTeX]

Problem set 4

[pdf, LaTeX]


Abel's Exercise set 1


Solutions to Abel's Exercise set 1


Abel's Exercise set 2



Project handout