APPPHYS 225: Probability and Quantum Mechanics (AY2008)

Tue+Thu 2:15-3:30pm / 126 McCollough


This course will introduce modern perspectives on fundamental aspects of quantum probability and will survey contemporary applications in quantum information science.  Parallels with classical probability will be emphasized in a way that clarifies quantum measurement theory and highlights practical utility.  A firm command of undergraduate quantum mechanics and familiarity with basic probability theory are assumed.




Final version: link


Reference materials


The following online materials will be utilized to provide supplemental reading for this course:


Introduction to Probability - Charles M. Grinstead and J. Laurie Snell : link
ACM217 notes: Stochastic Calculus, Filtering and Stochastic Control - Ramon van Handel : link


Please inform the instructor if you discover that either of these links disappears!


There are also a few published books that you might find relevant, but these will not actually be referenced explicitly in this course.


Class notes and assignments


Tue 9/23: Overview slides; class notes: classical probability review part 1
Thu 9/25:
Class notes: classical probability review part 2


Tue 9/30: Class notes: quantum states and measurements as a non-commutative probability model
Thu 10/2:
Class notes: generalized quantum measurement and POVM’s

Tue 10/14: Class notes: inference-disturbance tradeoffs in quantum measurement

Tue 10/21: Class notes: pure/mixed states, coherent superposition versus incoherent mixture
Thu 10/23:
Class notes: working with tensor products, partial projections and partial traces
Fri 10/24:
Class notes: operation elements from indirect measurement; partial trace example

Tue 10/28: Class notes: Projection Postulate from classical Bayes’ Rule in indirect measurement
Thu 10/30:
Class notes: CHSH inequalities; quantum versus classical correlation
Fri 10/31:
Class notes: quantum versus classical teleportation

Tue 11/4: Class notes: entanglement, Schmidt decomposition and quantum eraser
Thu 11/6:
Class notes: cloning and broadcasting
Fri 11/7:
Class notes: approximate cloning; locally immeasurable product bases

Tue 11/11: In class we discussed sections II.A-B and III.A.1-2 of:
S. D Bartlett, T. Rudolph and R. W. Spekkens, “Reference frames, superselection rules, and quantum information”
Review of Modern Physics, 79, 555 (2007).
Thu 11/13:
Class notes: linear representation of symmetry operations; encoding a direction in two spins
Fri 11/14:
Class notes: covariant POVM for estimating dihedral transformations

Tue 11/18: Class notes: probability models from symmetry considerations; also Section 1.2 of this book
HW assignment #8: read the following papers for the last week of class:
For Tue 12/2:
R. W. Spekkens (2007)
For Thu 12/4:
L. Hardy (2003) and J. Bub (2005)

Thu 12/4:
Class notes: state degrees of freedom, symmetric informationally-complete POVM’s

The End!