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Oct 1, 2021, 5:48:56 PM10/1/21

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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

"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

Oct 4, 2021, 3:16:21 AM10/4/21

to

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.
> So what should we do to describe quantum mechanically

> what people mean with classical transport?

>

Sylvia.

Oct 6, 2021, 3:23:44 PM10/6/21

to

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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