Re: Duplicates are Selves

From: scerir (scerir@libero.it)
Date: Wed Apr 09 2003 - 14:06:41 MDT

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    Robert Bradbury:
    > They should *not* have to be the same atoms (pointing out
    > a problem with one of Lee's "levels") but allows teleporting
    > to be an information transmission problem and not a matter
    > transmission problem (which gets more expensive).

    Polzik [1] realized a quantum entanglement between two caesium
    gas clouds, containing 10^12 atoms each. Entanglements of such
    large objects (containing similar, or identical, elements) enables
    *collective* properties (such as global spin) to be teleported
    from an object to another.

    But according to the usual teleportation protocol, to teleport
    a human body, information from each of those 10^30 atoms
    should be extracted, "trasferred", and reassembled elsewhere.
    Leaving the fidelity problem apart, this would require a *very*
    long time, of course.

    But - who knows? - some powerful trick might be hidden in an
    already well known mistery.

    Let us say we wish to communicate to a friend far away, or we
    wish to re-create a simple quantum state, i.e. like this one
          |psi> = cos l |up> + sin l |down> e^(i k)
    Here we have two real numbers, l and k. Thus, if we try to
    communicate this *known* quantum state, by classical means,
    we need an infinite - at least in principle - number of
    classical bits. And imagine the number of classical bits
    we must provide if we are trying to communicate, by classical
    means, or re-create a quantum state which is *unknown*!

    Now, if we try to teleport the same simple quantum state, *known*
    or *unknown*, it happens that teleportation can be achieved by
    transmitting (with classical means) just two (!) classical bits,
    provided, of course, we already set the usual teleporting set-up
    and protocol.

    Thus, there may be some possible mystery. But where? Well, this
    seems to be a true mystery, at present. Many authors try to
    locate the *missing* or the *extra* information.

    I.e. Vaidman [2] seems inclined to solve the mystery by means of
    (his version of) MWI. His idea is that the local measurement of
    the teleportation procedure splits the world in such a manner that
    in each of the worlds the state of the remote particle differs
    from the state to be teleported by some known transformation.
    The number of those worlds is small. And that explains why the
    information which has to be transmitted, by classical means,
    for teleporting a quantum state, is much much smaller than the
    information needed for the creation of the same quantum state.

    Lucien Hardy [3] there are reasons for believing that *non-locality*
    (in Bell's terms: non-local-causality; in Einstein's terms:
    non-separability) may play an important role in quantum teleportation.
    He seems (sometimes) to speculate that, when a quantum state is
    teleported to the remote location, the *missing* information
    (or some *extra* information) is being carried by the non-local
    properties of the entanglement itself.

    Barrett [4] suggests that the mystery is resolved if we consider
    the quantum state (to be teleported) as a description (Schroedinger
    used to call it a "catalogue") of an ensemble of systems, rather
    than a single system. But, imo, this position (statistical
    interpretation) is just a smooth version of Vaidman's position
    (MWI, which is the reification of the old statistical interpretation).

    There are many more papers about the same subject, of course from
    Steiner [5] but also from Popescu, Zukowski, Cerf, Gisin, ...

    At present everything seems to move around a certain idea of
    non-locality. Entanglement. Bell's theorem. Cloning. Teleportation.
    And hidden transmissions of informations :-)

    [1] Nature, 413, 400, (2001)

    [2] L. Vaidman
    Teleportation: Dream or Reality?
    http://arxiv.org/abs/quant-ph/9810089

    [3] L. Hardy
    Disentangling Nonlocality and Teleportation
    http://arxiv.org/abs/quant-ph/9906123

    [4] J. Barrett
    Implications of Teleportation for Nonlocality
    http://arxiv.org/abs/quant-ph/0103105

    [5] M. Steiner
    Towards Quantifying Non-Local Information Transfer:
    Finite-Bit Non-Locality
    http://arxiv.org/abs/quant-ph/9902014



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