From: *Bruno Marchal* <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>>
On 8 Aug 2019, at 13:59, Bruce Kellett <bhkellet...@gmail.com <mailto:bhkellet...@gmail.com>> wrote:

On Thu, Aug 8, 2019 at 8:51 PM Bruno Marchal <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>> wrote:

    On 8 Aug 2019, at 11:56, Bruce Kellett <bhkellet...@gmail.com
    <mailto:bhkellet...@gmail.com>> wrote:
    On Thu, Aug 8, 2019 at 7:21 PM Bruno Marchal <marc...@ulb.ac.be
    <mailto:marc...@ulb.ac.be>> wrote:


        What I use is the fact that when we have orthogonal states,
        like I0> and I1>, I can prepare a state like (like I0> +
        I1>), and then I am myself in the superposition state Ime>(
        I0> + I1>), Now, in that state, I have the choice between
        measuring in the base {I0>, I1>} or in the base {I0> + I1>,
        I0> - I1>). In the first case, the “parallel” history
        becomes indetectoble, but not in the second case, so we have
        to take the superposition into account to get the prediction
        right in all situations.


    I don't think this is actually correct. Take a concrete example
    that we all understand. If we prepare a silver atom with spin
    'up' in the x-direction, then a measurement in the x direction
    does not produce a superposition -- the answer is 'up' with 100%
    certainty. But is we measure this state in the transverse,
    y-direction, the result is either 'up-y' or 'down-y' with equal
    probabilities. This is because the initial state 'up-x' is
    already a superposition of 'up-y' and 'down-y'. When we measure
    this in the x-direction, there is no parallel history. When we
    measure in the y-direction, we get either 'up-y' or 'down-y'.
    MWI says that for either result, the alternative occurs in some
    other world. And that alternative result is just as undetectable
    as the 'down-x' result for the x-measurement.


    The pure state up-x is the same state as the superposition of
    up-y and down-y.
    Me in front of up-x and Me in front of up-y + down-y are only
    different description of the same state. When measuring that
    state in the x-direction, I don’t made that y-superposition
    disappears.


All you are saying here is that if you measure the up-x state in the x direction, the state does not change -- it is still a superposition of up-y and down-y. Of course, if the state is not changed it does not change. Tautologies are not very useful.

OK, but you are saying that “ When we measure this in the x-direction, there is no parallel history”, like if the superposition did disappear, that is why I remind the tautology. They did not.

The state can still be represented as a superposition in some other basis, true. But this fact is of no practical significance for the operation in question -- measurement of the x-polarization.

I think there is a basic confusion in your thinking between basis states and "other worlds". You want to maintain the fiction that descriptions in terms of alternative basis states are somehow "real". But descriptions are not physical states, relative or otherwise.


Let us use “superposition of state” instead. The word “world” has too much metaphysical implicit connotations.

You object to the use of the word "world" in order to cover this confusion between basis states and worlds. A parallel world is a well-defined concept. I have defined it several times, and the basic characteristics are orthogonality and non-interaction, inaccessibility. Expressing a state in terms of some alternative set of basis vectors is, of course, always possible, and that changes the superposition, but it does not change the original state. In particular, it does not create additional "relative states" or "worlds". The description of a state is not the state: changing the description does not change the state.

It is like your oft-repeated assertion that "2+2=4" is not the same as two plus two equals four. But they are the same, they are both just descriptions of the physical operation of adding two objects to two other objects and getting the result as four. Descriptions are not the things themselves.


In that case, if the computer run a superposition similar to the initial calculation in Shor algorithm (before taking the final Fourier transform on all superposed results), decoherence means that all computations are done on the superposed state.

That is not decoherence.

That is the massive parallelism, than we can exploit through the final Fourier Transform and measurement.

And all this parallelism occurs by simple rotations of the single state vector in Hilbert space.

Bruce

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