Re: quantum information and foundation

[zoran skoda <zskoda@gmail.com>]

Dear Prof. Joyal,

1. I agree with you that the hype about combinatorics of Feynman diagrams
is, while important for constructing good practial theories and
calculational methods, not appropriate target for understanding and changing
the very foundations of quantum theory.

2. I disagree with you that quantum groups have no applications to real
quantum physics. Surely, they do not change the very foundations of quantum
theory, but do have numerous and significant applications to concrete models
in quantum physics. Most of the significant applications are limited to the
quantum groups at root of unity. They appear as symmetries of numerous
integrable models, e.g. quantum spin chain models, and hidden symmetries of
some conformal field theories to name the most well-understood applications.
Harmonic analysis on quantum groups is important to calculate analytic
expressions for correlation functions in some of the models, and the
representation thoery at root of unity has a Kazhdan-Lusztig type
correspondence in some cases to vertex operator algebra representations.
This involves not a superficial but a very intricate picture.

As a physicist I despise when people come with quantum and string
terminology when not at least vaguely and indirectly appropriate,
revelations by mathematician that they found the true meaning of some
physical concepts and alike. A typical claim is of many mathematicians that
vertex operator algebras are THE SAME as conformal field theories, while
they feature just a part of the true story. I witnessed a talk by a young
hot mathematician who gave an introduction that CFT as a discipline is
a SUBSET of string theory. When I told him that CFT originated and is
fruitful outside of string theory too (e.g. in study of critical phenomena
in condensed matter physics), and thus should not be DEFINED subordinated
to its particular hot and popular application, he started substantiating his
claim waving hands that somebody has proved that "this and this is the same
as that and that" (I am not paraphrasing but citing!!! what kind of
psychology drives these young postdocs from Princeton-level hype places
snowing the audience with misterious claims and referal to untouchable
authorities whom they seen somewhere and half-understood ??).

3. As far as quantum computation and quantum information, the engineering
boundaries of the field are not natural place of subject within physics and
math. If one looks at the textbooks on quantum information more than half of
the books are just standard material on quantum physics, not a different
area. Topological quantum computation on the other hand, is more of
topology, monoidal categories and QFT-type in its technology so it is
already included in divisions listed. Various measures of coherence on the
other hand in the literature are rather nonrigorous and somehow trivial
variations are publiashable. I have been a referree  2 times and witnessed
extremely content-free papers building the merit on 2-3 elementary and
obvious observations which were claimed to have connections to algebaric
geometry etc. while the authors were not being able to say anything
nontrivial other than fancying about formal similarity in a polynomial
describing some quantity. The other referree, from optical engineering has
suggested the papers for publications as "significant" in J. Phys. A which
accepted it against my recommendations. Baisng publications on hype and
superficial remarks other than substantial content is a sign of an unhealthy
standpoint of the community. I agree with John Baez that there is a healthy
potential in quantum computing, but do not think that the area is
well-defined, not subsumed to already listed areas of applications (like
QFT), and would remark that it is overfunded for the present extent of true
significant research.

4. It is not very important how we subdivide the applications of categories,
but it is more important that we educate each other with aspects and
overview of the subjects some of us are not specialized in but others can
help. Awareness of possible applications amy help to bridge the gap between
special areas and main focuses of current pure research.  Thus while the
lists like the one compiled in this discussion may be fun to mobilize a bit
of cross-disciplinary discussion, more educative efforts and true
discussions would do more.


Zoran


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