From: scerir (scerir@libero.it)
Date: Fri Oct 25 2002 - 15:15:19 MDT
I do not know if the quantum cloning is relevant,
or not, in the present discussion. Maybe not (as
Eugene et al. pointed out).
Anyway, from the philosophical point of view, it might be
interesting to say there are, in theory, two kinds of quantum
cloning machines.
A deterministic quantum cloning machine, which performs
unitary operations (unitary evolution is deterministic).
A probabilistic quantum cloning machine, which performs
measurements and also unitary operations, with a
'postselection' of the measurement results (and copies
are produced with certain probabilities).
Now there are two quantum no-cloning theorems.
1. An arbitrary unknown state can not be cloned, deterministically
or probabilistically, since the linearity of quantum mechanics
forbids xoxing;
2. Deterministic cloning of non-orthogonal states is impossible
because of the unitarity of the evolution).
But these theorems do not rule out the possibility of *probabilistic*
cloning of non-orthogonal states. In example the states secretly
chosen (from a certain set) can be probabilistically cloned if
they are linearly independent. The probabilistic quantum cloning
machine yields perfect copies of the original states, but with
certain probabilities of success.
Due to the existing links between quantum no-cloning, no-ftl-signaling,
Heisenberg's principle (quantum cloning breaks this principle,
because you could measure position of a particle and momentum of
its clone!) it is interesting to check if a *probabilistic* quantum
cloning machine might ....
http://arxiv.org/abs/quant-ph/9704020
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