Physics 2205S
QUANTUM MEASUREMENT
(Special Topics in QO )

(updated on 9 January 2024)


Lecturer:

Aephraim Steinberg
(MP 1103, x8-0713 [don't bother trying this], email address [my last name][at][physics.utoronto.ca])
Lectures:

most Tuesdays and Thursdays 4:10-5:00, in MP 606
also some Fridays, 4:10-5:00 to be arranged, also in MP 606


Office hours: by appointment
Organizational meeting and first lecture: Tuesday, 9 January, 2024 (4:10pm in MP606)

Overview | Grading | Syllabus | Announcements | Reading | Lecture Notes | Assignments | Final Project


PLEASE SIGN UP AT THE PIAZZA COURSE PAGE AT piazza.com/utoronto.ca/winter2024/phy2205 --
Please sign up whether or not you're certain to take the course, and whether or not you're taking it for credit; doing so binds you to nothing.

Overview

This is a course intended for any students in Quantum Information, Quantum Optics, Quantum Control, or other disciplines who are interested in modern developments in the experimental side of fundamental quantum mechanics, such as (but not limited to) quantum information. It obviously assumes a good working knowledge of quantum mechanics, but new formalism will be introduced as needed, so it should be accessible to first-year as well as second-year graduate students.

Much of the mystery of quantum mechanics has been tied up with the famed "quantum measurement problem" (what is collapse? how/when does it occur? does it occur?), but nearly all of us have been trained with a very simplistic view of what quantum measurements really are. It turns out there are many different types of measurement in the real world, and almost never do they correspond to what we get from the QM textbooks. While the textbook treatments long appeared to be a fair simplification of reality, experimental advances in recent years have brought the study of quantum measurement out of the shameful realm of metaphysics and into the lab. Numerous experimental groups now study effects ranging from "interaction-free measurement" to "quantum non-demolition measurements" to "weak measurements" to "generalized quantum measurements" (POVMs), to "quantum cloning" and "quantum teleportation". Ideas about quantum measurement are central to the new fields of quantum cryptography and quantum computation (especially quantum error correction). There are even two distinct paradigms of quantum computation in which the effects of measurement itself are used to carry out operations, in the place of logic gates built from "real" physical interactions.

Course Structure and Grading

This will be something of a seminar-style course, and discussion and participation are expected.
As an advanced special-topics graduate course, it has no textbook, and while I will assign readings from time to time, you will be expected to do research on your own to learn the material. You will also be encouraged to suggest new readings or new topics to share with the rest of us, since the ones I have thought of are by no means exhaustive!

The course will culminate in individual research projects (probably for oral presentation, either during class or during a separately scheduled time, depending on the number of students). I hope that we will all learn at least as much from these as from my own lectures, so I see the purpose of my lectures as giving every one enough common background as a starting point for the discussion of current topics in experimental quantum measurement. The rest of the course, including the grading scheme, follows from this premise:



Syllabus

The syllabus is subject to evolution and diffusion (and hopefully your own influence), but below is a rough idea of where we will be going (I am likely to be unable to get to all of these topics, certain to decide some of the order should be changed, and very hopeful that you will help direct us to other topics I haven't thought of yet):
  1. Overview
  2. Mathematical background
  3. Interference and information
  4. Time and phase measurement
  5. Weak measurement
  6. Quantum state/process estimation/characterization
  7. Quantum information
  8. Quantum metrology and imaging
  9. POVMs (generalized quantum measurements)
  10. Continuous measurement and quantum feedback control
  11. ...topics suggested (and/or presented) by you!



Announcements

Reading

We will not be directly following any textbook.

Nonetheless, there are a number of excellent books I recommend you look at; in particular, Kurt Jacobs's Quantum Measurement Theory and its Applications. The first two chapters are available for free at http://www.quantum.umb.edu/Jacobs/books.html.
Chapter 1 and Appendix A contain a much more rigorous treatment of much of the formalism I will introduce rather cavalierly at the start of the course, so I strongly recommend taking a look at them ASAP. Various sections of chapter 2 are likely to be of great interest as well.

My own perspective is summed up in my Les Houches lectures, Quantum Measurements: a modern view for quantum optics experimentalists, and some of the early course material will follow this -- I recommend that you look at its first sections during the first week as well.
For a review of background material, you should of course have a copy of your personal favorite QM textbook (reasonable options include Basdevant & Dalibard; Shankar; Cohen-Tannoudji, Diu, & Laloë; Townsend).

For a general introduction to the historical issues in quantum measurement, you will probably be interested in the wonderful Quantum Theory and Measurement, edited by Wheeler & Zurek, Princeton University Press (1983).

If you haven't already done so, and want to understand quantum mechanics, you should also get around to reading the thin, inexpensive, and quick paperbacks

Additional references will be provided sporadically throughout the course (or by request if I get neglectful), via Piazza.


For a fuller treatment of the more rigorous and mathematical material, common references include

but I do not intend this to be a rigorously mathematical course, and I provide these references solely for the benefit of those who prefer them to my hand-waving.

Some light introductions to some of the topics we will discuss include Zurek, "Decoherence and the transition from quantum to classical," Physics Today 44, 36 (1991); Horgan, "Quantum Philosophy," Sci. Am. 267 (1), 94 (7/92); Quantum Optical Tests of the Foundations of Physics, A.M. Steinberg, R.Y. Chiao, and P.G. Kwiat, in the American Insitute of Physics Atomic, Molecular, and Optical Physics Handbook, edited by G.W.F. Drake, AIP Press, 1996 (the latter is available at http://www.physics.utoronto.ca/~steinber/Quantum_Optical.pdf).
Some references to my own group's recent work in quantum measurement can be found at http://www.physics.utoronto.ca/~aephraim/QMsmt.html. In particular, some of the course will deal with a particular obsession of mine, "weak measurement," a wordy description of which, along with a long list of references, may be found in Speakable and Unspeakable, Past and Future, A.M. Steinberg, in SCIENCE AND ULTIMATE REALITY: Quantum Theory, Cosmology and Complexity, edited by Barrow, Davies, and Harper.

For most of the course, the relevant references will be journal articles, and students will be expected to read additional articles on related topics and bring them up in class, via the email list (e.g. to suggest that I cover one in lecture), and in their final presentations.

Lectures


Final Presentations

The final presentations for PHY 2205 ("Quantum measurement") will be held through the week of 1 April, 2024.

Full schedule below or in pdf form here.

PHY 2205 Quantum Measurement: Final Seminars (week of 1 April 2024)

all presentations are 15 minutes long, followed by 5 minutes for questions/discussion.

Monday's presentations will be in MP 408;

all other days will be held in MP 606.

• Monday 1 April, 2:10-3:00 pm (MP 408)

2:10 – 2:25 : Aiden Rosenbush "The Mean King's Problem"

2:30 – 2:45 : Kai-Sum Chan "Quantum Error Correction and GKP states"

• Tuesday 2 April, 4:10-5:10 pm (MP 606)

4:10 – 4:25 : Zou Xiang "How does LIGO use squeezed quantum states to surpass the Heisenberg limit?"

4:30 – 4:45 : Pria Dobney "Spin squeezing in atomic clocks"

• Thursday 4 April, 4:10-5:10pm (MP 606)

4:10 – 4:25 : Noah Baker "Bell's Theorem using GHZ States: The Algebraic Proof and Experimental Demonstration"

4:30 – 4:45 : Rui Jie Tang "Quantum discord as a quantum resource"

4:50 – 5:05 : Lorenz Nieman "Quantum Darwinism: Emergence of classicality from the quantum realm"

• Friday 5 April, 4:10 pm-5:10pm (MP 606)

4:10 – 4:25 : Nicholas Sullivan "How to consistently treat interactions between classical and quantum systems"

4:30 – 4:45 : Tanmay Grover "Toric codes and quantum error correction"



Back to Aephraim

Steinberg's Home Page