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Dear all,
On the Bell experiment, I can only recommend Richard's latest papers, my own commentary just posted, and my recent contribution arXiv:2305.05299 [quant-ph]. For those that really want to go into the mathematics of my views, there is a longer paper on arXiv: 2305.06727 [quant.ph].
Inge
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On 24 May 2023, at 06:53, Chantal Roth <cr...@nobilitas.com> wrote:
Bryan,What about the counts in this example (maybe we can all agree and then move on :-))?There are 2 pairs of photons (total 4).The first pair registers as pol.The second pair registers as coh.What are your click counts?What is your total in this case?
<image.png>
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Attachments:
- image.png
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Hi,
I propose a solution to define the measures produced by the
pol/coh states.
It allows to interpret Bryan's equation E.
It requires to use the notion of detectable states that I
mentioned before.
The list of experimental measurements can be produced by the
following pol/coh states:
+ + +p +p / +c +c
+ - +p -p / +c -c
- + -p +p / -c +c
- - -p -p / -c -c
+ 0 +p +c / +p -c / +c +p / +c -p
- 0 -p +c / -p -c / -c +p / -c -p
0 + +p +c / -p +c / +c +p / -c +p
0 - +p -c / -p -c / +c -p / -c -p
0 0 +p +p / +p -p / -p +p / -p -p / +c +c / +c -c / -c +c / -c
-c
=> The same experimental measurement can be produced by
different pol/coh/detectability combinations.
A combination of pol/coh states can produce two types of
experimental measurement depending on whether pol or coh is
detected:
States / exp. measures
+p +p ++ 00
+p -p +- 00
+p +c +0 0+
+p -c +0 0-
-p +p -+ 00
-p -p -- 00
-p +c -0 0+
-p -c -0 0-
+c +p +0 0+
+c -p +0 0-
+c +c ++ 00
+c -c +- 00
-c +p -0 0+
-c -p -0 0-
-c +c -+ 00
-c -c -- 00
If the detectable state is 'pol' we measure:
+p +p ++
+p -p +-
+p +c +0
+p -c +0
-p +p -+
-p -p --
-p +c -0
-p -c -0
+c +p 0+
+c -p 0-
+c +c 00
+c -c 00
-c +p 0+
-c -p 0-
-c +c 00
-c -c 00
If the detectable state is 'coh' we measure:
+p +p 00
+p -p 00
+p +c 0+
+p -c 0-
-p +p 00
-p -p 00
-p +c 0+
-p -c 0-
+c +p +0
+c -p +0
+c +c ++
+c -c +-
-c +p -0
-c -p -0
-c +c -+
-c -c --
During an experiment, there are 16 possible pol/coh states:
=> 4 produce a pair measurement.
=> 4 produce no measurement.
=> 8 produce singles
However, during an experiment, we do not measure only 25% of
pairs.
The experimentally measured rates depend on the proportions of the
pol/coh states of the particles which is not 50% / 50%.
These proportions must depend on the interactions with the
filters.
This makes the theoretical equation E difficult to define if we
want to include the states pol + coh + detectability with mutually
exclusive combinations.
The equation of the form E = (Neq-Nnq)/(Neq+Nnq) used in
experiments can give a useful result only if we assume that
everything is detectable.
Otherwise, it expresses the result of a mixture.
If we consider non-detectable states, we should write E in the
following form.
Noting:
a = Neq detectable
b = Nnq detectable
a' = Neq not detectable
b' = Nnq not detectable
then:
E = ((a + a') - (b + b'))/((a + a') + (b + b')) (1)
We can then split the equation into two parts.
E = (a - b)/(a + a' + b + b') + (a' - b')/(a + a' + b + b') (2)
As the part on the right is not measurable (a' - b') = (0 - 0), we
only have
E = (a - b)/(a + a' + b + b')
If the detectability state is random with a pol,coh rate of
50%,50%, then probably a = a' and b = b' (to be established)
It will allow to write
E = (a - b)/(a + a + b + b)
We find Bryan's equation
E = (1/2)(a - b)/(a + b)
So according to me Bryan's equation has only an incomplete form
because it expresses only what is measurable with respect to what
is emitted, but should produce correct results.
The full form is (1).
Pierre
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Hi,
To define a pair detection it is necessary to detect two
particles, therefore two detections (events).
Two events produce a single pair measurement.
N_tot=N_eq+N_ne=(N_eq^p+N_eq^c)+(N_ne^p+N_ne^c)
Pierre
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On 26 Jun 2023, at 19:26, Bryan Sanctuary <bryancs...@gmail.com> wrote:
Hi Jan AkeI think my document is clear. It shows a boolean distinction between the two complementary attributes and which shows that this is consistent with the usual definition of the correlation. I do not have anything more to add. Please note the complementary nature of Eq.(9)
<image.png>Eq (31) shows that it is a weighted sum, via p_p and p_c as you seem to want, but the boolean feature of complementarity shows that the two add.I believe it is all consistent.Bryan
On Mon, Jun 26, 2023 at 1:01 PM Jan-Åke Larsson <jan-ake...@liu.se> wrote:
Dear Bryan,
Your formula (still) suggests the total correlation is a weighted average the "coherent" and "polarization" correlations.
But to generate the correlation you claim, you then add them together.
Could you please decide on one alternative only?
/Jan-Åke
On 2023-06-26 18:51, Bryan Sanctuary wrote:
Hello
I made a new video which is descriptive only, i.e. non mathematical
Below is my answer to the problem of adding or averaging the correlations from polarization and coherence.
Your comments are welcome
Bryan
<image.png>
<image.png>
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Sometimes I get confused because some words are used with a different meaning from my own use. For example, Bryan wrote in the “section” “Determining the correlation”:
“Polarization and coherence are complementary properties which means that they are not manifest simultaneously” … “…, if one contributes to the coincidences, the other does not.”
In my understanding coherence may have some meanings like, if two beams have a similar behavior they could interfere, or if photons have the same phase they can interfere, and so on. Photon coherence also means photon indistinguishability. Polarization is independent of coherence. No complementary aspects exist. A polarized beam may be coherent or not, there is no exclusive aspects involved – and even less “…, if one contributes to the coincidences, the other does not.”
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So Jan-Ake
Complementary outcomes occur randomly from a random source and so, one click at a time, they build up the usual statistical formula from the two complementary properties. At each detection, we have either delta_p or delta_c, and a contribution to the correlation from either. The probabilities, p_p and p_c simply express that over the experiment, a certain number are pol and a certain number is coh.
You are right, I never use this formula because I do not know the probabilities. However the formula expresses that two sources of clicks add the two correlations and agrees with the usual expresson for the correlation. I see nothing wrong with me.
Think of one click at a time.
Bryan
On 18 Aug 2023, at 00:40, Bryan Sanctuary <bryancs...@gmail.com> wrote:
<AnnilaWikstromEPRCorrelation.pdf>
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On 19 Aug 2023, at 01:44, Bryan Sanctuary <bryancs...@gmail.com> wrote:
Hi Jan-Åke and Richard,I neglected to add the authors of the paper I attached to my last email. So here I introduce Arto Annila and Marten Wikstrom who wrote Quantum entanglement and classical correlation have the same form.I have answered the question about the weighted average: here shows I can sum the two:
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<AnnilaWikstromEPRCorrelation (1).pdf>
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On 22 Aug 2023, at 17:26, Steve Presse <spr...@asu.edu> wrote:
May I recommend something very concrete assuming both Richard and Bryan agree.
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On 22 Aug 2023, at 10:37, Mark Hadley <sunshine...@googlemail.com> wrote:
However
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On 23 Aug 2023, at 15:58, Bryan Sanctuary <bryancs...@gmail.com> wrote:
On 23 Aug 2023, at 16:23, Steve Presse <steven...@gmail.com> wrote:
Richard you will not loose.
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On 23 Aug 2023, at 16:23, Steve Presse <steven...@gmail.com> wrote:
Richard you will not loose.
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Just a comment on Steve Press’ :
“When you
consider a joint probability distribution between two particles, with particles
indistinguishable, then you necessarily recover entanglement.
This effect is what leads to the fringe patterns of Young’s
to slit experiment, and what resolves the Gibbs paradox of statistical
mechanics.”
Fringe patterns occur because photons are within one coherence area of the field at the slits position. In other words, they are indistinguishable and, therefore, coherent.
Entanglement is something more and it happens, in case under discussion, over detection equipment separated by a large distance, not like the arrangement of close slits giving the fringe pattern.
Some extra detail may not be relevant at his moment, like the coherence area for an entangled pair is DIFFERENT from the coherence area for independent photons.
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On 23 Aug 2023, at 18:16, Bryan Sanctuary <bryancs...@gmail.com> wrote:
The initial entangled correlation is therefore distributed between a sum of the symmetric and anti-symmetric contributions originally seen in Equation (8).
On 23 Aug 2023, at 17:25, Bryan Sanctuary <bryancs...@gmail.com> wrote: