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  • "Classical transport"

    From Jos Bergervoet@21:1/5 to All on Fri Oct 1 14:48:53 2021
    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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  • From Sylvia Else@21:1/5 to Jos Bergervoet on Mon Oct 4 07:16:18 2021
    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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  • From Jos Bergervoet@21:1/5 to Sylvia Else on Wed Oct 6 20:23:42 2021
    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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