03 April 2000, “Foundations in the Light of Information” Below is a slightly modified version of the invitation letter I sent everyone. (The only change is an update on the attendance.) Looking forward to seeing you again. (BTW, I hope you'll take the problems list seriously.) Dear friends, Gilles Brassard and I are organizing a little meeting in Montréal from Wednesday May 17 through Friday May 19 on the subject of “Quantum Foundations in the Light of Quantum Information and Cryptography.” We hope you can come. Mainly the purpose of the meeting is to gather a group of our friends who think that some aspects of quantum foundations are a little more mysterious than they ought to be and, importantly, are intrigued by the idea of applying quantum information to the task of cleaning things up. The atmosphere of the meeting should be quite relaxed with plenty of time for discussion and/or private brooding: we only ask that you be prepared to give a 20 to 30 minute talk (though longer talks are welcome too) expressing your point of view and any avenues for progress you foresee. Attendants are also encouraged to compile and share a list of concrete problems whose solution would tell us something novel about the quantum foundations.
03 April 2000, “Foundations in the Light of Information” Below is a slightly modified version of the invitation letter I sent everyone. (The only change is an update on the attendance.) Looking forward to seeing you again. (BTW, I hope you'll take the problems list seriously.) Dear friends, Gilles Brassard and I are organizing a little meeting in Montréal from Wednesday May 17 through Friday May 19 on the subject of “Quantum Foundations in the Light of Quantum Information and Cryptography.” We hope you can come. Mainly the purpose of the meeting is to gather a group of our friends who think that some aspects of quantum foundations are a little more mysterious than they ought to be and, importantly, are intrigued by the idea of applying quantum information to the task of cleaning things up. The atmosphere of the meeting should be quite relaxed with plenty of time for discussion and/or private brooding: we only ask that you be prepared to give a 20 to 30 minute talk (though longer talks are welcome too) expressing your point of view and any avenues for progress you foresee. Attendants are also encouraged to compile and share a list of concrete problems whose solution would tell us something novel about the quantum foundations.
18 November 1997, “Bolt from the Blue” I saw Adrian Kent's four papers on the server early this morning, and I was reminded of Léon Rosenfeld's description of Bohr's reaction to the EPR paper: This onslaught came down upon us as a bolt from the blue. Its effect on Bohr was remarkable. We were then in the midst of groping attempts at exploring the implications of the fluctuations of charge and current distributions … A new worry could not come at a less propitious time. Yet, as soon as Bohr had heard my report of Einstein's argument, everything else was abandoned … I suspect the air in Montréal will be just as this when you all awake today. How I wish I were there to see the excitement! I hope for the sake of our field, and a generally more exciting world, that Kent is right! As you all know, this sceptical physicist (i.e., me) was always a little wary of the Mayers–Lo–Chau strong claim of having considered all possible quantum protocols. I would like to hear the Montréal verdict once it is in. A good day to all! 31 August 1999, “Subliminal Messages” Quantum Foundations in the Light of Quantum Cryptography Quantum Foundations in the Light of Quantum Cryptography Quantum Foundations in the Light of Quantum Cryptography Quantum Foundations in the Light of Quantum Cryptography
22 August 1999, “Your Article” I am writing to let you know that I enjoyed your article quant-ph/9812050, “Why Quantum Mechanics is Hard to Understand,” very much. I was in particular very pleased with your Section IV “Dynamics vs. History.” It may interest you to know that Markus Fierz expressed a similar point of view in his article: “Does a physical theory comprehend an ‘objective, real, single process’?” in Observation and Interpretation in the Philosophy of Physics , edited by S. Körner (Dover, NY, 1957), pp. 93–96. I will append the full text below for your enjoyment. [See note to Rüdiger Schack, dated 29 August 1999.] Most importantly, I would like to ask you for the final coordinates of your paper. Was it published somewhere? I would like to cite it in an upcoming paper. 28 August 1999, “Not Much” I don't have a good idea about where to send your paper. I think chances are that AJP will be tougher than FP . In any case, it had an impact on me. My old advisor used to say of our joint papers, “If three people read this paper, we'll be doing OK!” If you know of two others with yours, you're probably doing OK. I like this focus on the concept of “object.” I look forward to anything you might have to say about it. I have some slides that I use as a rallying cry to the idea that quantum information theory may have some impact on quantum foundations. The first is a list of axioms for quantum mechanics.
This document is the first installment of three in the Cerro Grande Fire Series. It is a collection of letters written to various colleagues, most of whom regularly circuit this archive, including Howard Barnum, Paul Benioff, Charles Bennett, Herbert Bernstein, Doug Bilodeau, Gilles Brassard, Jeffrey Bub, Carlton Caves, Gregory Comer, Robert Griffiths, Adrian Kent, Rolf Landauer, Hideo Mabuchi, David Mermin, David Meyer, Michael Nielsen, Asher Peres, John Preskill, Mary Beth Ruskai, Ruediger Schack, Abner Shimony, William Wootters, Anton Zeilinger, and many others. The singular thread sewing all the letters together is the quantum. Some of the pieces are my best efforts to date to give substance to an evanescent thought I see rising from the field of quantum information---I call it the Paulian idea. To the extent I have communicated its misty shadow to my correspondents and seen a twinkle of enthusiasm, it seemed worthwhile to expand the jury on this anniversary occasion.
17 January 2001, “First Contact” I am writing this letter to find out if you are interested in attending a conference in Växjö, Sweden this summer titled “Quantum Theory: Reconsideration of Foundations.” I do this because I have read a few of your papers and parts of your book on Bohr, and I have been extremely impressed. By trade, I am a practitioner of the new field of quantum information theory and computing – and indeed the main session I am organizing at the Växjö meeting will be about quantum foundations reconsidered in that light – but your description of Bohr's thought meshes so well with what I'm seeking in physics that I'd like to get you there too. PLEASE NOTE that this is not exactly a real invitation yet: I am still lobbying for a more philosophical contingent at the meeting. But, I would very much like to hear your reaction just as soon as possible. If things work out, and you would like to come, I will recontact you very soon with further details. The main reason I want you at our meeting is that I have this “madly optimistic” (Mermin called it) feeling that Bohrian–Paulian ideas will lead us to the next stage of physics. That is, that thinking about quantum foundations from their point of view will be the beginning of a new path, not the end of an old one.
April 1996, to Michiel van Lambalgen, “Thesis” About myself (in case you are wondering) I am a physicist. My research specialty is “quantum information theory,” a field that concerns a hodgepodge of things including quantum cryptography, quantum computing, and statistical inference problems having to do with quantum mechanical systems. You may have heard of some of these things through Paul Vitanyi or André Berthiaume (Vitanyi's postdoc). I am presently a postdoc working for Gilles Brassard and Claude Crépeau in Montréal; starting October, I will have a three year position at Caltech. I was once interested in the mathematics of randomness because, though I am Bayesian through and through for all other uses of probability, I believed that probabilities for quantum mechanical measurement outcomes were something different…in fact something more akin to the frequentist conception. Thus I put a lot of effort into studying von Mises, Church, Kolmogorov, Martin-Löf, Chaitin, etc. (I didn't find your papers until I had pretty much abandoned this belief, though I'm not sure that I am completely over it!) I had hoped that there might be some mathematical connection between the structures found in quantum theory (vector spaces, positive-operator valued measures, etc.) and the structures required to formalize the notion of random sequences…at least that was my motivation.
Quantum information is an emerging field which has attracted a lot of attention in the last fifteen years or so. It is a broad subject which covers from the most applied questions (e.g., how to build quantum computers or secure cryptographic systems), to the most theoretical problems concerning the formalism of quantum mechanics, its complexity, and its potential to go beyond classical physics. I have written these notes as an introduction to the formalism of quantum information, trying to show how it is a natural progression from an undergraduate course on quantum mechanics (just as I felt it was for me). Hence, these are mainly notes about the language of quantum information and the meaning of its terms, not about its applications. They do not intend to be an exhaustive review about the field, but just a logical sequence of ideas, concepts and definitions, building up towards the continuous variables formalism, which actually takes over most of the notes. In this way, most of the results are stated without proof, and I haven't been careful with references; this is a work in progress, and I intend to add such things in the future. In any case, most of the topics that I introduce have been thoroughly covered in previous books and reviews, and with this notes I only intend to give my point of view, as well as to introduce the different topics and objects in exactly the way I work with and think about them, hoping it will be useful, especially for the people who are starting in the field. These notes originated in 2010 as a way of studying for my close collaboration with Raúl García-Patrón and Nicolas J. Cerf, to whom I am deeply grateful for guidance and incredibly clarifying discussions. They benefited greatly as well from the weeks I spent in Doha with Hyunchul Nha and his group in 2012, especially from discussions with him and Ho-Joon Kim.