A "classical channel", or more general the concept of
"classical transport" is often used in Quantum Mechanics-
related experiments, or thought experiments. But it is
usually not entirely clear how it is defined.

If we assume that quantum mechanics is our theory, then
classical transport can only be quantum mechanical transport
of a special kind, since everything has to be described
by quantum mechanics. So what is special about it? And how
can we model it as something happening entirely within the
framework of quantum mechanics, for instance to describe
quantum teleportation completely within quantum mechanics?

Let us assume we have one qubit and we are asked to do
classical transport. Possible definitions/implementations
are:
1) It first has to be measured, meaning that it will
become entangled with at least one other qubit in our
system (that's measurement, quantum mechanically!) and
then we send this other qubit by classical transport (so
we haven't gained much in terms of a definition..)
2) Just transport the qubit quantum mechanically, but
assume that along the way it gets entangled with at
least one external-world qubit. (This seems not clear
enough unless we also specifically preserve some
information along a chosen axis..)
3) Just transport the qubit quantum mechanically, but
assume the phase relation between its 2 components gets
lost, i.e. adding a random phase to the components but
maintaining their magnitudes. (Requires a preferred
axis, as it should, but requires "throwing dice" which
I'd like to avoid since it cannot happen in unitary
time evolution.)
4) As in 3), but in addition to losing the phase now
also assume that the magnitudes are lost, by collapsing
them, to [1, 0] or [0, 1], presumably both still with a
random phase applied to it. (This requires even more dice
throwing and involves a collapse of the state, so it cannot
happen in quantum mechanics. Collapse is only "apparent".)

So what should we do to describe quantum mechanically
what people mean with classical transport?

--
Jos

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On 02-Oct-21 7:48 am, Jos Bergervoet wrote:

So what should we do to describe quantum mechanically
what people mean with classical transport?

Ordinary communication with a speed of light limitation.

Sylvia.

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On 21/10/04 9:16 AM, Sylvia Else wrote:

On 02-Oct-21 7:48 am, Jos Bergervoet wrote:

So what should we do to describe quantum mechanically
what people mean with classical transport?

Ordinary communication with a speed of light limitation.

That definition does have the merit of simplicity.

But then "classical" in classical transport does not have to be
specified (since it is just ordinary). And we think all possible
forms of transport and communication are limited by the speed of
light, which further simplifies the definition: classical transport
is just transport, and classical transport of information is just
transport of information!

Still I don't think it can be correct. More likely seems this:

1) Classical transport (of information) obeys the Bell inequality
for the amount of mutual information between receiver and sender
after the transport. With signaling limited by the speed of light.

2) Ordinary transport means any QM-allowed transport, so the limit
is now the Tsirelson bound (which for a qubit is sqrt(2) times
higher than the Bell limit. Signaling is still light-speed limited.

3) Supra-quantum transport is for example the Popescu-Rohrlich [1]
behavior, with for the correlations again a factor sqrt(2) higher
bound (so already a factor 2 higher than what "classical" allows!)
But even that example only allows light-speed-limited signaling.

4) More extreme supra-quantum transport, i.e. even further away from
currently accepted physics, might even (finally) allow superluminal
signaling. But with that we would be digressing far from the topic..

It seems to come down to what "ordinary" means. If that is case 2),
than logically case 1) would need specifying by a qualifier like
"classical".

[1] See "Popescu-Rohrlich box" <https://en.wikipedia.org/wiki/Quantum_nonlocality#The_physics_of_supra-quantum_correlations>.

--
Jos

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