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I was hoping you guys could recommend reading material on Quantum Information Science. First off, here's my background.

Personally, I started reading Ballentine's Quantum Mechanics and I found it be a very consistent book in terms of foundations and absolutely loved it. The treatment is better than most other books on the subject, including the popular ones like Sakurai, Merzbacher. I wondered why there existed this difference. Why were the others rather sloppy?

I found my answer when I discovered my new favorite author, Asher Peres. As I read his works, I found this quote in an excellent paper (Rev. Mod. Phys., 76, 2004)

"Quantum mechanics is used by theorists in two different ways. It is a tool for computing accurate relationships between physical constants, such as energy levels, cross sections, transition rates, etc. These calculations are technically difficult, but they are not controversial."

The other group is tackling the foundations. I was drawn towards this group and as I read more of Peres' works, I got absorbed with the idea of information in QM. I then read many of C. Fuchs' works and followed on with those in the Perimeter Institute, where this sort of research seems to be hot.

Coming from the background of Peres and Ballentine, my gut reaction to books which talk of collapse or simultaneous measurements or quantum mechanics of individual systems as opposed to ensembles is to shut them. Only slowly am I overcoming this, because I find that most books are very sloppy and that if I wish to learn any more, I cannot afford to do so. I am trying to be as open as possible.

Currently, I am reading the book by Busch, Lahti and Grebowski, notes on Arxiv by Keyl and also the notes by Preskill. If anyone has any suggestions, recommended reads, I'd love to know!

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It is absolutely incorrect to think quantum mechanics only describes ensembles. The quantum state of a single hydrogen atom predicts many definite things about its motion, and the wavefunction of the electron is a physical thing--- that's what you feel when you knock your hand against a table. The idea that it is sloppy to treat the wavefunction as a complete description of a physical system is just an error of thinking, and if your sources commit it, please try to switch to other sources which are more "sloppy" in your view, because you will come to understand that they are not sloppy at all. –  Ron Maimon Feb 2 '12 at 12:19
    
@Ron Maimon: When we knock at a table, we feel not the wave function of an electron but the density matrix of a many-electron system. As statistical mechanics reveals, it is a density matrix (namely $e^{-S/k_B}$) that describes a single macroscopic system - not wave functions, which are not observable. –  Arnold Neumaier Mar 2 '12 at 19:32
    
@Arnold Neumaier: This is incorrect. As you go to absolute zero, the hardness of the metal is unchanged (if anything it becomes harder), and in the limit of zero temperature there is a unique ground state wavefunction, which is computable to good approximation by current techniques. Wave-functions are observable in prepared systems, with many copies. Even in a macroscopic system, any wavefunction which has an appreciable probability is good enough to give the repulsion, the density matrix does not give you new states, just a probability distribution on old ones. –  Ron Maimon Mar 3 '12 at 2:45
    
@Ron Maimon: What is incorrect? A metal at any temperature is described by a mixed multielectron state, not by the wave function of an electron. For each single piece of metal, there is only a single density matrix, not a multitude of wavefunctions. None of the latter is observbable (they are not even uniquely determined by the state), while the former is. –  Arnold Neumaier Mar 3 '12 at 16:08
    
@Arnold Neumaier: The wavefunction is a wavefunction of all the electrons, not of one electron. At zero temperature, the density matrix might as well be a wavefunction, because it is a single pure state, the ground state. The ground state wavefunction and the ground state density matrix are identical information. What you are saying is that I mixed up the multi-electron wavefunction with the single-electron wavefunction, which is a terrible error, I agree, but one that I did not make. –  Ron Maimon Mar 3 '12 at 18:37
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7 Answers

Nielsen, Chuang: Quantum Computation and Quantum Information

Bengtsson, Życzkowski, Geometry of Quantum States

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Hi, Thanks, but I already know of those two. Any other suggestions? –  WiFO215 Jan 31 '12 at 4:00
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You might like quantiki http://www.quantiki.org/, it is a portal dedicated to quantum information theory. It contains interesting stuff ( e.g, video abstracts of papers).

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Thanks, but I knew of this too. I was hoping there'd be something I missed. –  WiFO215 Jan 31 '12 at 21:30
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I'd recommend the lecture notes from these two courses taught by John Watrous. They can be found at http://www.cs.uwaterloo.ca/~watrous/lecture-notes.html from when he taught at the University of Calgary. I've used the notes from his Theory of Quantum Information course numerous times for a quick reference on some more difficult concepts.

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The notes from his course at the University of Waterloo are also great. –  Chris Ferrie Feb 27 '12 at 22:07
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Scott Aaronson has just published a new book about quantum computing. According to the nice introductary comments the author himself has written to his book here (scroll down to the second half of the article if you only want to learn about the book), it should explain and introduce both the physical and mathematical concepts quantum computing is based on.

Maybe reading this book can help students in choosing the appropriat mathematical and phyics lectures to be heard in what reasonable order to finally being able to do research in quantum computing too.

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+1 I'm on p. 85 (of 370) and thus far it is a delight. I suggest perusing the first pages ("Critical Review") using Amazon's "Look Inside" feature to assist you in your purchasing decision. –  Glen The Udderboat Apr 14 '13 at 10:34
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The best recommendation I can offer isn't for a book, but a series of video lectures. The Perimeter Institute and the University of Waterloo offer a Masters program in theoretical physics called Perimeter Scholars International (full disclosure: I graduated from PSI in 2010), and videos of all PSI lectures are posted on PI's video site, PIRSA. One of the PSI courses, Rob Spekkens' course on quantum foundations, sounds like it'd be the exact kind of thing you're looking for. The most recent offering of his class can be found here.

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I know of these too. I like Spekkens' course and also Ben Schumacher's course. Chris Fuchs lectures are very inspiring and informative. –  WiFO215 Feb 3 '12 at 10:43
    
Would you happen to know any references for Statistical Mechanics books which introduce stat mech from the perspective of information theory? –  WiFO215 Feb 7 '12 at 14:26
    
The online book ''Classical and Quantum Mechanics via Lie algebras'' (lanl.arxiv.org/abs/0810.1019) has in Chapter 10: Models, statistics, and measurements a discussion on the relation of statistical mechanics to information theory –  Arnold Neumaier Mar 2 '12 at 19:07
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Have you seen Quantum Computer Science : An Introduction by Mermin? It is a really fine book.

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This book is the clearest and most straightforward introduction that I've seen. –  Nick Thompson Apr 14 '12 at 12:47
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I have found a resource on my own. Here are lectures from H. Mabuchi at Stanford:

http://www.stanford.edu/~hmabuchi/AP225-2008/

and R. Sasaki:

http://www.stanford.edu/~rsasaki/AP226/AP226.html

Both have excellent lecture material uploaded.

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