Physics 2206S
EXPERIMENTAL QUANTUM MEASUREMENT
(Special Topics in QO )
(last updated 11 April 2012)
Lecturer:
Aephraim Steinberg (rm 1103, x8-0713, email address [my last name][at][physics.utoronto.ca])
Lectures: Tuesdays and Thursdays 3-4, in MP 408.
Office hours: tentatively Wednesdays 2-3, in MP 1103.
Organizational meeting and first lecture: Thursday, 12 January, 2012
Overview |
Grading |
Syllabus |
Announcements |
Reading |
Lecture Notes |
Assignments |
Final Project
IMPORTANT MESSAGE: Blackboard gives me convulsions, so I will maintain the course web page here - however, please register on the Blackboard page (I believe I have set it so that you can do so yourself) in order to be on the course email list.
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.
This is a course intended for any students in Quantum Optics 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.
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:
- 50% of your grade will be based on the final presentation (30% for the presentation itself, 10% for your handling of questions, and 10% for your participation during the other presentations).
- To ensure that every one masters the basic "background" material before the latter part of the course, there will be a one-hour midterm approximately 2/3 of the way through the course, accounting for 35% of your grade.
- To help prepare for the midterm, there will be several problem sets during the early part of the course, and these will account for the reamining 15% of your grade. They are intended as practice, and not principally as a component of the course evalutation; the 15% is merely a bribe. They will be graded on a simplistic 3-point scale (serious effort / half-hearted attempt / inadequate). Questions raised by the problem sets which you fail to resolve on your own should be excellent fodder for the class discussions, so please raise them in class. You are also welcome to discuss them in more detail with me during my office hours, which are tentatively Wednesday 2-3.
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):
- Overview
- Mathematical background
- Measurement and the projection postulate
- Density matrices and reduced density matrices
- von Neumann measurements and back-action
- Entanglement and decoherence
- Interference and information
- Feynman's rules for interference
- Which-way information and complementarity
- Quantum erasers and EPR experiments
- Equivalence of collapse and correlation pictures
- Interaction-free measurement
- Time and phase measurement
- Optical phase versus quantum phase
- Does a single photon have a phase?
- Does a laser, or a BEC, have a phase before it is measured?
- Superselection rules and reference frames
- Weak measurement
- Interaction-free measurements (again) and Hardy's Paradox
- Which-way measurements and quantum erasers (again)
- Applications?
- Quantum state/process estimation/characterization
- State and process tomography
- Squeezing and measurement-induced squeezing
- Measures of entanglement and nonlocality
- Quantum information
- Bell-state measurement
- Quantum error correction
- The "no-cloning" theorem
- Dense coding and teleportation
- Measurement-driven computation
- the quantum search algorithm
- Quantum metrology and imaging
- spin-squeezed states, atomic clocks, et cetera
- "N00N" states, Heisenberg-limited interferometry, et cetera
- "ghost imaging"
- classical analogs... is there truly a quantum advantage?
- POVMs (generalized quantum measurements)
- non-orthogonal state discrimination
- the mathematical definition
- compass states and metrology
- SIC-POVMs, MUBs, tomography, and quantum states
- Continuous measurement and quantum feedback control
- The "watched pot never boils" effect (AKA "quantum Zeno effect") and the anti-Zeno effect
- Continuous probing of a quantum system
- Quantum feedback
- ...topics suggested (and/or presented) by you!
Please sign up on the Blackboard page so that you will be on the course email list.
There is no textbook.
Nonetheless, Kurt Jacobs has a textbook in preparation at Cambridge University Press, An Introduction to Quantum Measurement Theory, and several chapters are available at http://www.quantum.umb.edu/Jacobs/books.html; it is quite possible
that if this book were already out it would be the textbook, but if
nothing else, it is likely to be the most relevant background reading.
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, and I look forward to seeing other chapters as they appear!
For the more basic 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
- Feynman's QED: the strange theory of light and matter, and
- Bell's Speakable and unspeakable in Quantum Mechanics.
Additional references will be provided sporadically throughout the course (or by request if I get neglectful), and will be collected on this page.
For a fuller treatment of the more rigorous and mathematical material, common references include
- von Neumann's Mathematical Foundations of Quantum Mechanics
- Braginsky, Khalili, and Thorne's Quantum Measurement
- Helstrom's Quantum Detection and Estimation Theory,
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.
Much of this course will be based on a
lecture series I gave a few years ago; the powerpoint files for those lectures can be found at http://www.physics.utoronto.ca/~steinber/QMP.html.
Depending on how far I deviate from them and how organized I get, I may post new slides or lecture notes as time goes on.
24 January:
- recommended reading list related to two-photon interference and quantum erasers can be found here. Remember that this is intended as a starting point and you should continue reading on your own.
- some readings about EPR and Bell can be found here.
- some readings about the non-cloning theorem can be found here.
26 January:
There is a new review on the arXiv by Masanao Ozawa, which provides an extremely mathematical, axiomatic approach to modern quantum measurement theory. We will not even approach this level of mathematical rigor in lectures, but I recommend that you all at least read some of the paper, and those of you with a mathematical bent will probably be interested in reading the entire thing:
Mathematical foundations of quantum information: Measurement and foundations, by Masanao Ozawa.
Introductory lecture (12 January, 2012)
Lecture 2 (17 January, 2012)
Lecture 3 (19 January, 2012)
Lecture 4 (24 January, 2012)
Lecture 5 (26 January, 2012)
Lecture 6 (31 January, 2012)
Lecture 7 (2 February, 2012)
Lecture 8 (7 February, 2012)
Lecture 9 (9 February, 2012)
NOTE: I will be out of town on 16 February, and 21-23 February fall during Reading Week, so there will be no lectures, but you should begin exploring topics for your final project (see below), as well as catching up on the references from the lectures so far, in preparation for the midterm.
Lecture 10 (14 February, 2012)
Lecture 11 (28 February, 2012)
Lecture 12 (1 March, 2012)
Lecture 13 (6 March, 2012)
Lecture 14 (13 March, 2012)
Lecture 15 (15 March, 2012)
NOTE: I will be out of town on 20 and 22 March, and there will be no lectures.
Lecture 16 (27 March, 2012)
As I emailed, I strongly encourage you to read Lobino et al, Science 322, 563 - 566 (2008), to see a modern example of process tomography and how it is related to the various quasi-probability distributions, but also as background for upcoming discussions of quantum metrology et cetera.
Lecture 17 (29 March, 2012)
Problem set 1 assigned 24 January, 2012; due 31 January, 2012.
Problem set 2 assigned 14 February, 2012; due 28 February, 2012.
The final presentations will be held during the last two weeks of term, starting around March 27th. You have been asked to send me a proposed topic before the end of Reading Week, when you should begin investigating your topic. Further information and some potential topics, for inspiration, can be found at this link.
SCHEDULE for remainder of term (as of March 12):
March 13: lecture 14
March 15: lecture 15
March 20-22: I'm away
March 27: lecture 16
March 29: lecture 17
April 3 - 12: four days of presentations
(last week of term + next two days, if still no objection)
April 3:
Graham: Quantifying and Distinguishing Entanglement
Nicolas: Quantum Discord
April 5:
Shreyas: Reflection of a particle from a quantum measurement
Carolyn: Experimental quantum cloning
April 10:
John: The "Mean King" problem
Dan: Kochen-Spekker and contextuality
April 12:
Matin: Weak-value amplification
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