[Tim May, in another thread]
Any finite system, which of course all systems are, can have all of its
quantum mechanics calculations done with finite-dimensional vector
spaces. The full-blown machinery of an infinite-dimensional Hilbert
space is nice to have, in the same way that Fourier analysis
[Joao Leao]
What we lack is a genuinely quantum model of
computation that could be mathematically tractable as the Turing or Post
models and can account for entanglement in all its glory.
As far as I know you can describe certain classes of entanglement
by means of Borromean rings, which are
On Tuesday, December 31, 2002, at 07:02 AM, Joao Leao wrote:
I don't agree with Tim's suggestion that infinite-dimensional Hilbert
spaces
are somewhat ancilliary in QM and that all systems are calculable in
finite dimensional modes. In fact infinite sets of spaces are the rule
in
QM and
the
Tim:
Werner's course that you point out is geared toward Quantum Information
applications and so the emphasys on finite spectra is understandable from
the
context. My point is that, in conventional quantum mechanics intro courses,
you begin with problems like the harmonic oscillator or the
[scerir]
As far as I know you can describe certain classes of entanglement
by means of Borromean rings, which are beautiful and sometimes
also unpredictable.
I realize that Kauffman already wrote something ...
http://www.math.uic.edu/~kauffman/QETE.pdf
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