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    Quantum Teleportation Of Cats
    By Sascha Vongehr | May 15th 2011 06:48 AM | 5 comments | Print | E-mail | Track Comments
    About Sascha

    Dr. Sascha Vongehr [风洒沙] studied phil/math/chem/phys in Germany, obtained a BSc in theoretical physics (electro-mag) & MSc (stringtheory)...

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    Time to reveal the solution to the cat killing mystery introduced in “If Schrödinger's Cats All Die, Do the Alive ones go to Hell?” and further explained in “Rotating Schrödinger's Cat to Death”. The solution is a huge letdown for all cat haters. Instead of being send to hell or at least into a parallel universe where they won’t bother no more, the cats stay right here in our lab! (See Nina – I am not as bad as you think.)


    Remember, the question was: If we interact with the Schrödinger cat inside the box so that we will only have dead cats result, what do the alive cats see? There must be a place into which those cats can jump. However, it cannot be the outside of the box that they went into, because that outside includes the experimenter, and the experimenter only observes dead cats.


    The answer to the question is surprisingly simple. In short: To do what was discussed, we need a very elaborate setup in order to prepare the photons that are directed into the box. In order to definitively retrieve a dead cat from the experimental box while the alive cat does not notice a thing, the |Alive> cat must quantum teleport out of the experimental box and into the photon-preparation setup. Where do the alive cats jump out; what do they see if the box opens? They see the photon-preparation room; that is where they jump out!


    You may object: “Wait a minute – now there are at least two cats every time, namely a dead one in the experimental box, and the same one, dead or alive, in the photon-preparation room.


    This is indeed the moral of the story. If we want to achieve what we set out to do, there is no other way. It is a lesson about the in popularity rising quantum teleportation, which is widely misunderstood and which I plan to demystify further in future posts.


    Let us now get into the meat of the explanation – there is no shortcut to the lazy ones shorter than this:


    The kill-mechanism involved a single initial photon (different from the many photons send in later by the photon-preparation setup) that was put into a superposition state. If we want to change the state inside the box so that only dead cats result, we must effectively let the dead and alive cats re-interfere. In other words, we must effectively resurrect the state as it was before the dead/alive decision occurred inside the box. We must effectively resurrect the initial photon. “Effectively” is again meant in the sense explained in “Rotating Schrödinger's Cat to Death”.



    In order to let the states effectively re-interfere, we must take care of, or in some sense know of all the so called decoherence terms, that is all the entanglement that the two photon states have undergone with the cat. In other words, we would need to “know” the complete state of the cat in its entirety, because only then is there any chance to revert all the entanglement. In order to know the cat completely however, we need an exact copy.


    We assumed linear quantum evolution as it has been observed by experiment, which means the no-cloning theorem as proved by Wootters and Zurek [1] holds. We cannot copy any quantum state. There is only one method to have two quantum states that are exactly the same: Prepare (make) the whole state completely twice.


    Recall that the problem was clearly stated in a way so that the |Alive> cat does not notice something intrusive is happening. The whole problem is only mysterious if the cat after three minutes still really sees the box starting to open and expects that the laboratory is still out there. If your method to kill the cat is noticed by the |Alive> cat state, then it is neither the |Alive> cat state as discussed by Schrödinger, nor is it at all interesting: If the cat notices being killed in any way, you might as well just shoot it – no quantum physics required.


    If the cat is not to notice the diminishing of the probability of her ever leaving the experimental box, the photon-preparation setup must already have something inside that knows the complete state of the cat in the experimental box, something that is effectively a copy. When the photons interact with the inside of the experimental box, the box and the photon-preparation setup become entangled, exactly like it is known from quantum teleportation.


    If you want the alive cat to not notice anything, you must effectively teleport the superposition state out of the experimental box and into the photon-preparation set-up.


    --------------------------------------------------

    [1] W. K. Wootters and W. H. Zurek, Nature299, 802 (1982)

    Comments

    MikeCrow
    So, this is a sort of Star Trek teleporter.

    The only question is what do we do with all the dead bodies?
    Never is a long time.
    vongehr
    Quantum teleportation is precisely not like a Star Trek teleporter. Those who write that now science even came up with teleportation just like SciFi predicted, plainly do not grasp the physics [(like a certain featured writer on Science2.0 who thinks she can regurgitate popular science rubbish when it is about physics but makes a huge humdrum if scientists do not use the exact same definition of "creativity" as she does (probably so to discredit anything more creative than her stale "art")]. They called it "quantum teleportation" for a reason.
    MikeCrow
    First I realize state of the art of quantum teleportation is maybe teleporting the state of a single atom (I think I remember seeing an article making that claim).

    But in your hypothetical scenario you make a point of saying you are encoding the state of the entire cat.

    In other words, we would need to “know” the complete state of the cat in its entirety

    If that ever become possible, it would still not be a Star Trek teleporter, because you end up with a dead body every time. Hence my reply which was suppose to be a funny quip.
    Never is a long time.
    rholley

    The Arnold Cat Map



    Eeuw-pop-eeeeuw! What’s that in the hall?
    Six little mices are having a ball,
    ’Coz the cat has been 
                                          which is quite undeserved.
    But wait!  Arnold’s Cat Map says volume’s conserved,
    In phase space at least – thank you, Arnold, for that,
    For we may now get back our poor pussy cat.
    Sorry, wee mices, you’ve just gotta go.
    Eeuw-pop-eeuw, Eeuw-poppô.

    Robert H. Olley / Quondam Physics Department / University of Reading / England
    vongehr
    Thanks for these pictures. They indeed kind of transport the meaning of "decoherence for all practical purposes". It is totally scrambled, but in principle, with the right transformation, the cat is still perfectly the same and could be gotten back into shape. Moreover, for the cat state itself, it knows nothing about how scrambled up she may appear relative to other observers. We are in a sense fundamentally all screwed up in such ways, the quantum universe being much like picture 132, while all cats are in there in some way, relative to themselves seeing nothing suspicious that could hint at any scrambling - all with much poetic license plus a pound of salt of course.