[extropy-chat] random links

[scerir]

"spike":

> > Prime numbers peep in.
> > http://www.arxiv.org/abs/quant-ph/0212084

> But this link isn't about prime numbers, [...]

Yes, Zelinger's paper is about information,
quantum, and related philosophies.

But the quote below comes from that paper.

"How to define the total information content
of more complex systems? In a n-dimensional Hilbert
space, one needs n^2 -1 real parameters to specify
a general density matrix rho, which must be
hermitean and have Trace(rho) = 1. Since measurements
within a particular basis set can yield only n - 1
independent probabilities (the sum of all probabilities
for all possible outcomes in an individual experiment
is one), one needs n + 1 distinct basis sets
to provide the required total number of n^2 - 1
independent probabilities. Ivanovic (1981) showed
that the required number n + 1 of unbiased basis sets
indeed exists if n is a prime number."

The existence of unbiased basis sets is interesting 
both for fundamental reasons (is a quantum mechanics 
without probability amplitudes possible?) and for the
construction of quantum-information protocols (key 
distributions based on a large number of unbiased 
basis sets may have advantages over key distributions 
based on qubits).

So prime numbers peep in both for fundamental reasons
and for 'technological' reasons. (But at least the latter 
is difficult stuff for me).

s.