> On 5 Aug 2019, at 15:12, Bruce Kellett <[email protected]> wrote:
>
> On Mon, Aug 5, 2019 at 10:37 PM Bruno Marchal <[email protected]
> <mailto:[email protected]>> wrote:
> On 5 Aug 2019, at 14:13, Bruce Kellett <[email protected]
> <mailto:[email protected]>> wrote:
>> On Mon, Aug 5, 2019 at 6:07 PM Bruno Marchal <[email protected]
>> <mailto:[email protected]>> wrote:
>> On 5 Aug 2019, at 03:27, Bruce Kellett <[email protected]
>> <mailto:[email protected]>> wrote:
>>> On Sat, Aug 3, 2019 at 10:52 AM Jason Resch <[email protected]
>>> <mailto:[email protected]>> wrote:
>>> On Fri, Aug 2, 2019 at 7:33 PM 'Brent Meeker' via Everything List
>>> <[email protected]
>>> <mailto:[email protected]>> wrote:
>>> On 8/2/2019 5:12 PM, Jason Resch wrote:
>>>> On Fri, Aug 2, 2019 at 6:51 PM 'Brent Meeker' via Everything List
>>>> <[email protected]
>>>> <mailto:[email protected]>> wrote:
>>>
>>> Wherever it happens, it's one world. Worlds are things things that are
>>> orthogonal on to one another so that's why they're separate. I don't know
>>> what Deutsch believes.
>>>
>>>>> In any case, you have still managed to avoid the question of the reality
>>>>> of the 10^1000 intermediate computational states. I won't press for an
>>>>> answer if you don't have one.
>>>>
>>>> I already gave the answer. There is only one intermediate state. It just
>>>> happens to have lots of components in the basis you used to express it.
>>>>
>>>> And each of those components represents a trace of a computation performed
>>>> on one of the many possible values of the input qubits, do they not?
>>>
>>> That's one way of representing them. Just as citing the Fourier components
>>> of a firecracker going off shows the many components of the sound.
>>>
>>> That would be a convincing counterpoint, except here this "way of looking
>>> at the many components" performs a computation that would not otherwise be
>>> possible if all the atoms of the universe were mustered to perform the
>>> computation.
>>>
>>> The fact is that it is possible. The 2^n dimensions of the Hilbert space
>>> for n qbits is ample space for the computations. The trouble with looking
>>> to parallel worlds to do the computations is that there are an uncountable
>>> infinity of possible bases for the Hilbert space. What picks out just one
>>> base to represent all these parallel worlds? That is the real problem. You
>>> are ignoring the basis problem, just as Deutsch does. You naively assume
>>> that the computational base that you used to set up you quantum computer in
>>> the first instance is the only possible basis in which to view it. If you
>>> take the view that the single ray in Hilbert space represents all that is
>>> possible to know about the QC, and that computations are nothing more than
>>> rotations of this state ray in the space, then all these silly notions of
>>> parallel worlds evaporate.
>>
>> But then the interference between different branch of the universal ray,
>> whatever base is used to describe it, will disappear.
>>
>> No they won't. […] The rotations in this space cause exactly the necessary
>> interferences.
>
> It is a functional space, the ray describes all relative histories, and in
> the case of an observer looking a a superposition, the ray describes the
> observer being superposed itself. Shor algorithm exploits this.
>
> That is a really weird thing to say. The ray in Hilbert space is a concise
> description over the basis vectors. Whatever you do in some basis is
> reflected exactly in the ray representing the state. Conversely, whenever the
> state vector is rotated, the representation in terms of the basis vectors is
> changed correspondingly. They are not two distinct things. The point of
> thinking in terms of the state vector is that this is independent of the base
> chosen, so is a more objective way of looking at things.
>
> Think of a simple example. In general relativity we have the static spacetime
> given by Schwarzschild solution which describes a black hole. In the standard
> Schwarzschild metric, there is a 1/(r - 2M) term, so it appears that there is
> a singularity at the horizon (r = 2M). Eventually it was realised that this
> is merely an artefact of the coordinate system -- the horizon is not really
> singular, as can be shown by going to Kruskal or Eddington-Finkelstein
> coordinates, which are both smooth at the horizon. Working in a particular
> coordinate system (or set of basis states) is always fraught with ambiguity
> (the 'preferred basis' problem), so the actual situation is best represented
> by the state vector itself.
>
> The thing about the Hilbert space vector describing the quantum computer is
> that there is no observer involved. Since, in order to maintain coherence,
> there cannot be any external observer. So it is just meaningless to claim
> that "in the case of an observer looking a a superposition, the ray describes
> the observer being superposed itself.”.
Maybe in some dualist theory of mind. I am just using the idea that O(a+b) = Oa
+ Ob, where O is an observer not interacting with a superposition state.
In that state, O has still the choice to look at this in the {a, b} base, or in
the {a+b, a-b} base. In the first, the universal ray will describe ((O seeing
a) a + (O seing b) b) (well normalised),
Bruno
>
> Bruce
>
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