On 8/6/2019 2:51 AM, Bruce Kellett wrote:
On Tue, Aug 6, 2019 at 7:23 PM Bruno Marchal <marc...@ulb.ac.be
<mailto:marc...@ulb.ac.be>> wrote:
On 6 Aug 2019, at 10:28, Bruce Kellett <bhkellet...@gmail.com
<mailto:bhkellet...@gmail.com>> wrote:
No, you are just attempting to divert attention away from the
fact that you have no answer to my original argument that a
quantum computer can quite reasonably do the calculation by
rotating the state vector in Hilbert space, and consequently,
there is no need to imagine a large number of parallel worlds in
which the calculations are performed by a series of clunky linear
processing Turing machines. The hypothetical observer is entirely
irrelevant.
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 seeing b) b)
(well normalised),
A change of base does not make the idea that there are parallel
worlds any more convincing. Again, this is just a diversionary
tactic.
You are a bit too much fuzzy for me. I don’t see how a rotating
ray in an Hilbert space fail to described superposition states,
and without wave collapse the local (partial trace description) of
the situation above makes the superposition of the observer states
not eliminable.
I do not understand your objections here. They make no sense. All I am
claiming is some basic facts about vector spaces. If you have a vector
space, you can form an arbitrary number of sets of basis vectors that
span the space. Any vector in the space can be described in terms of
its projections onto these basis vectors. Correspondingly, any set of
values along the basis vectors can be summed to give a single vector
(or ray) in the space. Any change to either the basis vector
components, or the vector itself, is reflected in the other
representation. In other words, change the vector and you change the
projections on to the basis. Or change these basis components and you
change the vector.
In the case of a quantum computer, description of the calculation in
terms of some set of basis vectors is completely captured in the
corresponding changes to the summation vector. Consequently, the
description of the QC action in terms of some set of basis vectors is
entirely unnecessary -- the same action of the QC is entirely captured
by the unitary rotations of the summation vector in the Hilbert space.
That is all that there is to it. The advantage of the vector
description is that such a description is independent of the chosen
basis -- what happens to the vector can be described in terms of any
one of the infinite number of possible alternative bases. This is the
basis ambiguity, or problem of a preferred basis. To pick out one set
of base vectors and claim that these vectors represent a set of
parallel worlds in which the computations actually occur, is simply
unnecessary -- description in terms of the single summation vector
eliminates this stupidity.
Maybe you can tell me what happens in that situation. Note that
even after measurement, we can get back the interference effect by
erasing the memorised outcome of the result. Without collapse pure
state remains pure, and decoherence is relative to each “copies”
of the observer in the terms of the (universal)
These observations are entirely beside the point. You cannot erase the
memory of the result because memory is intrinsically irreversible.
Quantum erasure is a technical matter that occurs only in highly
constrained situations. I think you should catch up on some recent
work on quantum foundations, in which Everett does not necessarily
require the continuing purity of the quantum state. Measurement
changes the pure state into a mixture. Zureck has made considerable
progress in this direction in recent years. Quantum foundations has
moved on since 1957.
Bruce
The basis enters into a quantum computation only at the end, when the
algorithm requires that the answer be projected onto a specific basis.
Brent
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