From: scerir (scerir@libero.it)
Date: Tue Apr 08 2003 - 16:18:38 MDT
On Friday, April 04, 2003 10:16 AM
Lee wrote:
> So, I'll just go back to my former claim: if you believe physics
> with all your heart, and so don't suppose that the particular atoms
> that you are composed of have anything to do with who you are, then
> you won't mind teleporting, because the pattern of atoms will be
> the same after as before.
The point, imo, is 'fidelity'.
In 1993 [1] Bennett et al. defined the concept of quantum
teleportation, so. " [...] we show how Alice can divide the
full information encoded in |phi> into two parts, one purely
classical and the other purely non-classical, and send them
to Bob through two different channels. Having received
these two transmissions, Bob can construct an accurate replica
of |phi>. Of course Alice's original |phi> is destroyed
in the process, as it must be to obey the no-cloning
theorem. We call the process we are about to describe
teleportation, a term of science-fiction meaning to make
a person or object disappear while an exact replica
appears somewhere else." [2],[3]
Now it can be shown [4] that, due to the no-cloning
theorem, we can get a *local* quatum trasfer or a
*remote* quantum teleportation of one quantum
state, with a fidelity f > 2/3, just if we destroy
the original. It can be shown, also, that without
destroying the original, we can realize a *local*
quantum cloning, or a *remote* quantum faxing,
of several copies (from 2 to n), but in the
fidelity range of 1/2 < f < 2/3.
Thus, due to the linearity of quantum algebra,
and due to Heisenberg's relations, it seems very
difficult to reach, locally or remotely, by deterministic
or even by probabilistic means, a perfect xoxing,
that is to say to have a perfect copy of a quantum state,
or a perfect copy of an atom.
Btw, it seems possible to improve the fidelity factor
coupling entanglements (between systems) with
relativistic movements (of these systems). But for
now it is just fiction.
In Zeilinger's opinion within few years we could
teleport molecules. Polzik et al. already realized
entanglements between caesium gas clouds containing
(each) 10^12 atoms. But due to the (low) fidelity factor
it seems (to me) that in the future we could realize
an efficient polymorphism, faxing molecules up and down,
to the outer space.
[1] Phys. Rev. Lett., 70, 1895, (1993)
[2] Asher Peres, How the no-cloning theorem got its name,
http://arxiv.org/abs/quant-ph/0205076
[3] THe no-cloning theorem, by Wootters and Zurek,
1992, states that no information can be cloned in
the case of a number of (quantum) states equal or
greater than 3. The proof goes, essentially, this way.
Let us have a cloning (xoxing) machine with an initial
state |X_initial>, a vacuum state |vacuum>, a photon
with a polarization which is a linear superposition
like |ver>+|hor>. Due to linearity of quantum algebra,
it is not possible to get something like
|X_initial>|vacuum>(|ver>+|hor>) =
= |X_after>(|ver>+|hor>)(|ver>+|hor>)
[4] Cerf et al in Phys. Rev. Lett., 85, 1754, (2000);
Gisin, in Phys. Lett., A210, 157, (1996).
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