Re: quantum information and foundation

[Bob Coecke <Bob.Coecke@comlab.ox.ac.uk>]

Dear Andre, Thorsten, Dusko, and others,

Andre Joyal wrote:

> Quantum information science is also quite speculative:
>
> http://en.wikipedia.org/wiki/Quantum_Information_Science
> http://en.wikipedia.org/wiki/Topological_quantum_computer

It depends whether one is talking about:

(1) having a quantum computer in the shops
(2) theoretical discovery and experimental verification of new physical
phenomena inspired by approaching nature in information-theoretic terms.

While the first is indeed pure speculation, the second is a fact, with
many recently discovered physical phenomena, some of which are embodied in
terms of computational models, having effectively been established in the
lab.  Well-known examples are quantum teleportation and quantum key
exchange.  To mention one example of a phenomenon embodied in terms of
computational model: the ability to universally alter the state of quantum
systems by only relying on observations (= the measurement-based quantum
computational model).

Actually, certain guises of quantum information technology are effectively
available for purchase at:
ID quantique: http://www.idquantique.com/
MagiQ: http://www.magiqtech.com/MagiQ/Home.html
Smart Quantum: http://www.smartquantum.com/SmartQuantum.html
These three companies are not at all controversial, as opposed to for
example D-Wave.

There must be well over 1000 researchers active in the area which has its
`own wikipedia': http://www.quantiki.org/wiki/index.php/Main_Page

The general expectation would be that it are the quantum communication
protocols which will be the first transitions to mainstream technology,
and these may become components within some hybrid information processing
device.

Andre Joyal wrote:

> But the mystery of quantum physics lies elsewere: the extraction of a
> probability distribution from the complex values of a wave function.

Thorsten Altenkirch wrote:

> I agree that the big question in quantum theory is the "measurement
> problem".

The measurement-based quantum computational model is interesting in that
it considers what for a long time was the most controversial ingredient of
quantum theory, as the main processing resource: von Neumann's projection
postulate which describes how the state changes under observation.  These
changes under observations of typically highly entangled states can be
conveniently modeled by certain interacting Frobenius algebras in monoidal
categories:
http://arxiv.org/abs/0906.4725
http://arxiv.org/abs/0902.0500
I don't see any speculation here, just a convenient manner of representing
physical phenomena which effectively have been observed in the lab, by
using structures which are considered as category-theoretic.  A software
package to help with this is also under development:
http://web.comlab.ox.ac.uk/people/Aleks.Kissinger/projects.html
http://dream.inf.ed.ac.uk/projects/quantomatic/

In this context, recently Ross Duncan and Simon Perdrix solved an open
problem in the area of measurement-based quantum computing, which has
to do with guarantying a deterministic answer for certain sequences
of measurements, and the formulation of the answer crucially relies
on the Frobenius algebras.  (their paper is forthcoming)

Dusko Pavlovic wrote:

> most physicists would probably say that they are happy with hilbert
> spaces. but many of them (albeit mostly theoreticians) ar enot.

In fact, it are the experimentalists which tend to get quite excited about
the use of graphical languages to describe quantum phenomena since
these are more `operational' than the usual Hilbert space treatments.

Theoretcians have a harder time to denounce the things to which they are
used, except when you are called John von Neumann and you crafted the
Hilbert space quantum mechanical formalism a few years earlier.

Best wishes for the new year, Bob.



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