Entanglement and teleportation

[vanesch]

Ok it's relevant. :)

You've got a source producing entangled photon pairs
with the polarization unchanging from pair to pair.

This is the state |mdr_a> |mdr_a> if I understand you well. Technically this is not called an "entangled" state, but a product state (but that doesn't mattter for the discussion here).

You rotate polarizer_a, whose setting we'll
denote as p_a, to find the maximum
detection rate at A. Denote this setting as
MDR_a and the detection rate at MDR_a as mdr_a.
Denote the detection rate at A for any p_a as
dr_a. dr_a should vary (mdr_a --> 0) as
|p_a - MDR_a| varies (0 --> pi/2) as
the function,

dr_a = mdr_a(cos^2 |p_a - MDR_a|).

Up to here, I agree. That's also what I wrote.

Using the same conventions at B,
if MDR_b = MDR_a, then if mdr_b = mdr_a,
then the rate of coincidental detection,
denoted as cd_AB should vary (mdr --> 0)
as |p_a - p_b| varies (0 --> pi/2) as
the function,

cd_AB = mdr(cos^2 |p_a - p_b|).

No, this is not correct (according to quantum mechanics).
cd_AB = mdr cos^2(p_a-MDR_a) cos^2(p_b - MDR_a).

You can see this easily when you calculate the in - product of the ket of the joint detection (<a|<b|) with the state of the light |mdr_a>|mdr_a>, squared, which gives you the probability of observing this (joint) state. But note that it takes on (in this case) the form of a product of the detection probabilities at A and at B respectively (I didn't put this in, it came out of the QM calculation, but it is a result of the fact that the initial state was not an entangled state but a pure product state).

cheers,
Patrick.

 

[Sherlock]

No, this is not correct (according to quantum mechanics).
cd_AB = mdr cos^2(p_a-MDR_a) cos^2(p_b - MDR_a).

We've set p_a = MDR_a and are varying p_b so,

cos^2(p_a - MDR_a) = 1, and |p_b - MDR_a| = |p_b - p_a| so,

cd_AB = mdr{cos^2 |p_b - p_a|).


So, what about thinking of the detection that
initiates a coincidence interval as being aligned
with the (global) emission polarization?

 

[vanesch]

We've set p_a = MDR_a and are varying p_b so,

cos^2(p_a - MDR_a) = 1, and |p_b - MDR_a| = |p_b - p_a| so,

cd_AB = mdr{cos^2 |p_b - p_a|).

Ah, sorry, I missed that in your previous message. Yes, then it is correct.

So, what about thinking of the detection that
initiates a coincidence interval as being aligned
with the (global) emission polarization?

Do you mean: IF I have a detection at A, then necessarily the incident light must be parallel to a ? Then the detection rate at A (with fixed incident polarization) wouldn't follow Malus' law as a function of a. Indeed, you see yourself that if a is not perfectly aligned with the incident, fixed polarization, we still get clicks at A (diminished by a factor given by Malus' law). So these clicks start coincidence intervals when the incident light is NOT aligned with the global emission polarization in this case. The global emission polarization is, say, 0 degrees (fixed) by the source, and a = 45 degrees. They are clearly not aligned, nevertheless, there is still a click rate which is half of the MDR at A.


cheers,
Patrick.

 

[Sherlock]

Do you mean: IF I have a detection at A, then necessarily the incident light must be parallel to a ? Then the detection rate at A (with fixed incident polarization) wouldn't follow Malus' law as a function of a. Indeed, you see yourself that if a is not perfectly aligned with the incident, fixed polarization, we still get clicks at A (diminished by a factor given by Malus' law). So these clicks start coincidence intervals when the incident light is NOT aligned with the global emission polarization in this case. The global emission polarization is, say, 0 degrees (fixed) by the source, and a = 45 degrees. They are clearly not aligned, nevertheless, there is still a click rate which is half of the MDR at A.

For the coincidence interval initiated by a detection at A,
the maximum photon flux, ie., the maximum detection rate, mdr_a,
is 1. So, the polarizer setting at A, (p_a), is MDR_a for that
interval.

So, assuming a definite but randomly varying global polarization
produced at emission, the math seems to be telling us that the
qm projection along the transmission axis of the polarizer
associated with a coincidence-interval-initiating detection must
be parallel to (or at least *very* closely aligned with) the
global polarization of the light incident on the polarizers
for any given coincidence interval.

 

[vanesch]

For the coincidence interval initiated by a detection at A,
the maximum photon flux, ie., the maximum detection rate, mdr_a,
is 1. So, the polarizer setting at A, (p_a), is MDR_a for that
interval.

Wait, wait... I thought that the MDR_a was obtained when we were TESTING different a values, and then found the a value of maximum intensity ! Which will of course correspond to the polarization direction of the polarized source. With the same source, we can now CHANGE a to another, set value, and we will still have a detection rate (smaller than mdr_a). So you cannot claim that each click then corresponds to an event where the source polarization is coincident with a because the source has fixed polarization, and we changed a from that polarization.

So, assuming a definite but randomly varying global polarization
produced at emission, the math seems to be telling us that the
qm projection along the transmission axis of the polarizer
associated with a coincidence-interval-initiating detection must
be parallel to (or at least *very* closely aligned with) the
global polarization of the light incident on the polarizers
for any given coincidence interval.

Yes, and that's the "magic" of course. Because classically this cannot be, and the proof of that is exactly what I said above (and in at least 5 posts before): for a source with a FIXED polarization (of which we KNOW the polarization and which is NOT randomly varying), it is clearly not true that on a click, this means that the source polarization is parallel to the detected polarization. So if it is not true for a fixed source, why should it suddenly become true for a random varying source ?

cheers,
Patrick.

 

[Sherlock]

For the coincidence interval initiated by a detection at A,
the maximum photon flux, ie., the maximum detection rate, mdr_a,
is 1. So, the polarizer setting at A, (p_a), is MDR_a for that
interval.

Wait, wait... I thought that the MDR_a was obtained when we were
TESTING different a values, and then found the a value of maximum intensity !

In one case (nonvarying source polarization) dr_a varies as you vary p_a, and in
the other (randomly varying source polarization) dr_a doesn't vary as you vary p_a.
In either case we can get a value for mdr_a and MDR_a for any interval.

Which will of course correspond to the polarization direction of the polarized source.

That seems like an ok assumption (sort of obvious even), but
it's unnecessary for the formulation I've presented.

With the same source, we can now CHANGE a to another, set value, and we will still
have a detection rate (smaller than mdr_a).

In the first case (where dr_a varies with p_a), yes. In the
other, no, because dr_a doesn't vary with p_a.

So you cannot claim that each click then corresponds to an event where
the source polarization is coincident with a because the source has fixed
polarization, and we changed a from that polarization.

Making the assumption that MDR_a is aligned with
the source polarization doesn't change the formulation
or affect cd_AB, so long as MDR_b = MDR_a.

We can ascertain for sure in either case whether
p_a = MDR_a and MDR_b = MDR_a. If so, and assuming
independence of A and B, then the product of the individual
probabilities for any given interval matches the qm
prediction for rate of coincidental detection --
that is, you get a maximum visibility Malus' Law
angular dependence for cd_AB.

... for a source with a FIXED polarization (of which we KNOW the polarization
and which is NOT randomly varying), it is clearly not true that on a click,
this means that the source polarization is parallel to the detected polarization.
So if it is not true for a fixed source, why should it suddenly become true for
a random varying source ?

If you assume that MDR_a (for fixed source) is parallel
to the source polarization, then if p_a is set at MDR_a,
then it would mean that on a click the source polarization is
parallel to the detected polarization. For a randomly
varying source any p_a = MDR_a, because dr_a doesn't vary
as you vary p_a.

For setups where dr_a and dr_b vary with the polarizer
setting, the assumption that MDR_a is aligned very close
to the polarization of the incident light seems warranted.

For setups where dr_a and dr_b don't vary with the polarizer
setting, the assumption that MDR_a is aligned very close to
the polarization of the incident light is a bit of a problem,
in that this assumption would seem to imply that the polarizer
won't transmit a wave (or wavetrain or wavepacket) of sufficient
amplitude to trigger a detection if it is offset from the
polarization of the incident light by more than say a few degrees.

So, I guess I'll shelve that assumption for the time
being -- unless you can think of (or think up) a setup
where a photon detector only registers when the analyzing
polarizer is aligned to within a few degrees of the
(known) polarization of the light incident on the
analyzing polarizer.

We did show, however, that in setups where,

dr_a = mdr_a(cos^2 |p_a - MDR_a|), and

dr_b = mdr_b(cos^2 |p_b - MDR_b|), then if

mdr_a = mdr_b = mdr, and MDR_b = MDR_a = p_a, then

(normalizing mdr to 1)

cd_AB = (dr_a)(dr_b) = (cos^2 |p_a - p_b|).

This ports to the Bell type setups
with randomly varying source polarization, and
duplicates the normalized qm prediction for rate
of coincidental detection as the product of
the individual detection probabilities -- which does
not contradict the locality assumption
(causal independence of A and B).

MDR_b = MDR_a = p_a is necessary. This indicates
a common or global polarization parameter. Since
the assumption that this global polarization
parameter is a property of the light incident
on the polarizers isn't contradicted by the
formulation, there's no reason to assume that
it isn't produced at the emitter.

So, do we get any points for locality here,
or what? :)

 

[vanesch]

We did show, however, that in setups where,

dr_a = mdr_a(cos^2 |p_a - MDR_a|), and

dr_b = mdr_b(cos^2 |p_b - MDR_b|), then if

mdr_a = mdr_b = mdr, and MDR_b = MDR_a = p_a, then

(normalizing mdr to 1)

cd_AB = (dr_a)(dr_b) = (cos^2 |p_a - p_b|).

Yes, I agree that in the special case where p_a = MDR_a (that the source is aligned with polarizer A) you can write your formula. I do not agree with your MDR_a = MDR_b formula however, for a randomly oriented source, because you've been cheating: you've redefined MDR_a (which was initially the common polarization of the light) into a parameter of the intensity ; intensity which is constant and hence a parameter which is degenerate. Indeed, for a randomly oriented source, WITHOUT your formulas, I can write: dr_a = 1/2 and dr_b = 1/2 and then I apply cd_AB = dr_a x dr_b = 1/4. What's wrong with THAT then ?

But I'll tell you why there is no reason to assume that the source is aligned with the polarizer if we have a random source. If a polarized source is aligned with the polarizer, then the intensity WITH or WITHOUT the polarizer is the same (so MDR_a is the intensity of the beam, with or without polarizer). If you have a randomly oriented source, then MDR_a is indeed independent of the direction, but only HALF of the intensity with a polarizer).
So it is not that you "cannot distinguish" a randomly polarized beam from one that "follows the orientation p_A = MDR_a": indeed what counts is the ratio of the intensity before and after the polarizer. In the case of a polarized source, this is given by Malus' law, in the case of a randomly oriented source, this is 1/2.

cheers,
Patrick.

 

[Sherlock]

Yes, I agree that in the special case where p_a = MDR_a (that the source is aligned
with polarizer A) you can write your formula.

We don't need to make any assumptions about the source polarization.

We're just counting photons (detections) for specific intervals
and polarizer settings.

The formulation is general. It should apply to any setup where
you're counting photons and you have crossed linear polarizers analyzing
light from a single emitter.

The goal was to see if the qm prediction (wrt Bell-type setups)
can be written as the product of the individual probabilities at the
spacelike separated detectors. Apparently it can. So, this
would seem to support the idea that they are causally independent
wrt each other.

Of course this still doesn't tell us anything specific about the
physical nature of quantum entanglement.

But, the idea that the entanglement is created at the emitter
can't be ruled out on the basis that the only way you can get
the qm prediction in the form of the product of the
individual probabilities is if spacelike separated
events are causally affecting each other superluminally.

That is, you can make the assumption that the observed entanglement
is (at the level of the light) due to a global parameter of the incident
light, and that this parameter is produced at emission, and that
assumption won't alter the results of the formulation.

I do not agree with your MDR_a = MDR_b formula however, for a randomly oriented source, because you've been cheating: you've redefined MDR_a (which was initially the common polarization of the light) into a parameter of the intensity ; intensity which is constant and hence a parameter which is degenerate.

MDR_a hasn't been redefined. MDR_a is the polarizer setting, p_a,
associated with the maximum detection rate, mdr_a,
for a given interval. (Maybe the notation is confusing.
The uppercase MDR_a means a polarizer setting, and the
lower case mdr_a means the photon flux or detection rate
at that setting.)

It means the same thing in either the random or fixed setup.

We found that when dr_a varies as you vary p_a, then the
full (qm) visibility coincidence curve requires
that p_a = MDR_a = MDR_b.

With a random source, dr_a is the same for any p_a.

So, with a random source, any p_a = MDR_a = MDR_b.

Indeed, for a randomly oriented source, WITHOUT your formulas, I can write: dr_a = 1/2 and dr_b = 1/2 and then I apply cd_AB = dr_a x dr_b = 1/4. What's wrong with THAT then ?

It isn't general.

This is:

dr_a = mdr_a(cos^2 |p_a - MDR_a|)

dr_b = mdr_b(cos^2 |p_b - MDR_b|)

If we find that dr_a = mdr_a for any p_a, then
any p_a = MDR_a (and we might infer that the incident
light is randomly polarized at the source -- at least
for the A side).

Now, if dr_a and dr_b are the same for
any p_a and p_b (and especially
when p_a = p_b), then MDR_b = MDR_a, mdr_b = mdr_a,
(then we can infer that not only is the source
random, but also that our setup is ok), then (if dr_a
and dr_b are causally independent of each other)
the rate of coincidental detection,
cd_AB, should vary from mdr --> 0 as,

cd_AB = mdr(cos^2 |p_a - MDR_a|)(cos^2 |p_b - MDR_b|),

which for a random source reduces to,

cd_AB = mdr(cos^2 |p_b - p_a|),

as |p_b - p_a| varies from 0 --> pi/2.

For a setup where dr_a and dr_b vary as you vary
p_a and p_b, respectively, we should find that

cd_AB = mdr(cos^2 |p_b - p_a|)

only when p_a = MDR_a = MDR_b.

But I'll tell you why there is no reason to assume that the source is aligned with the polarizer if we have a random source. If a polarized source is aligned with the polarizer, then the intensity WITH or WITHOUT the polarizer is the same (so MDR_a is the intensity of the beam, with or without polarizer).

We don't need to know the detection rates without the polarizer(s).
The formulation doesn't require it.

If you have a randomly oriented source, then MDR_a is indeed independent of the direction, but only HALF of the intensity with a polarizer).

It doesn't matter what the photon count is sans polarizer(s).

MDR_a is the p_a where dr_a = mdr_a. mdr_a is the maximum dr_a.

We want a generalized formulation for calculating cd_AB as the
product of dr_a and dr_b.

In order to do that we need a generalized formulation for dr_a and dr_b.

We're not referencing the emitter or the light in the
formulation. We're just counting detector registrations wrt
different polarizer settings and (keeping the duration of the
runs at the different polarizer settings constant).

We might infer that a source is random or fixed from the results, and
for convenience we refer to the setups as random or fixed source, but
we don't need to.

So it is not that you "cannot distinguish" a randomly polarized beam from one that "follows the orientation p_A = MDR_a": indeed what counts is the ratio of the intensity before and after the polarizer. In the case of a polarized source, this is given by Malus' law, in the case of a randomly oriented source, this is 1/2.

In the formulation I presented, we can see that the photon count
without polarizers is not necessary.

What counts is the relationship between the photon count associated
with p_a and the photon count associated with p_b.

This way of looking at it has revealed that wrt rate of
coincidental detection, cd_AB, the full visibility Malus' Law angular dependence can be reproduced in a special case of a fixed
source -- which special case corresponds to any and all cases
of a random source.

 

[Sherlock]

Saying things like that the polarization is "irrelevant" for P(A,B) is clearly
wrong as you now see yourself, from the moment that the source is polarized.

It cannot be "irrelevant" for one case, and "of course dependent" in the other,
when the analyzing technique is identical (and only the source changes, which was
exactly what we were trying to analyze).

So clearly P(A,B) cannot be only a function of theta, but must depend also on the
angle between the polarization direction of the source and a and b, in this case.
But according to your claims, it is always the same value, no matter what the
incident polarization, as long as theta is a constant.

We can suppose that the primary rotational plane of
the incident light is aligned with the polarizer setting
that produces the maximum detection rate when the
detection rate varies with the polarizer setting.
If the detection rate is the same when the polarizers
are aligned, then we keep one polarizer fixed at the
max rate setting and offset the other to get coincidental
detection rates at various values for Theta (|p_a - p_b|).
If we offset the fixed polarizer from the max rate
setting so that the rate at the fixed polarizer is
a certain percentage of the max rate (n%mdr) less than
the max rate, then Theta will produce a similar angular
dependence skewed to fit into a range of values for cd_AB from
mdr - n%mdr --> n%mdr.

So, once the setting for the fixed polarizer has been
established, then the only thing determining the rate of
coincidental detection is Theta.

In the setup where detection rate doesn't vary
with the polarizer setting, specific values for
Theta produce the same cd_AB no matter what the
setting of the fixed polarizer. So, is the source
polarization relevant wrt determining cd_AB in this
type of setup?

 

[vanesch]

We can suppose that the primary rotational plane of
the incident light is aligned with the polarizer setting
that produces the maximum detection rate when the
detection rate varies with the polarizer setting.

That is not correct. We can only say so when, upon rotation, the detection rate varies from a maximum to a minimum which is 0. In that case, the incident light is completely polarized (with fixed polarization).

If the detection rate is the same when the polarizers
are aligned, then we keep one polarizer fixed at the
max rate setting and offset the other to get coincidental
detection rates at various values for Theta (|p_a - p_b|).

Again, this is not correct. It is only in the case of entangled photon pairs. In the case of classical, identical light, it is only correct when the light is fully polarized. For instance, it is not correct when you shine unpolarized light onto a beam splitter and look at the two outcoming beams (which DO have identical polarization at each instant of course because being a split beam). When you perform this experiment, you find rates which are INDEPENDENT of theta (as well, independent rates individually, as coincident).

If we offset the fixed polarizer from the max rate
setting so that the rate at the fixed polarizer is
a certain percentage of the max rate (n%mdr) less than
the max rate, then Theta will produce a similar angular
dependence skewed to fit into a range of values for cd_AB from
mdr - n%mdr --> n%mdr.

Again, this is not, in general, correct. Let us take incident light of fixed polarization. When the angle p_b is such that it is perpendicular to this direction, NO counts are seen at B, so no coincidences are observed.

So, once the setting for the fixed polarizer has been
established, then the only thing determining the rate of
coincidental detection is Theta.

Yes, that is true of course, FOR A GIVEN POLARIZATION PROPERTY OF THE SOURCE. If the source is polarized along a certain direction L, and you have fixed p_a, then of course you will find a coincidence rate which is only dependent on theta (because you have FIXED L and p_a).
However, for another value of L, and another value of p_a, you will find ANOTHER FUNCTION of theta.
Also, for a randomly polarized beam (no L anymore) and a given p_a, you will again find another function of theta. This time, however, by symmetry, for a different value of p_a (but the same "kind" of random polarization), you will find the same function of theta. However, that function of theta doesn't have to be the one you found for a polarized source. And it doesn't have to be the same if our random polarization is: 1) random and independent on both sides A and B ; 2) a mixture of identical polarizations at A and B 3) an entangled polarization at A and B.
You have 3 different formula for the 3 different cases.

In the setup where detection rate doesn't vary
with the polarizer setting, specific values for
Theta produce the same cd_AB no matter what the
setting of the fixed polarizer. So, is the source
polarization relevant wrt determining cd_AB in this
type of setup?

It is, in the derivation of cd_AB.

Again, explain me the difference between:

1) the production of entangled states (which do give us a cos^2(p_a - p_b) dependence, but that's a pure quantum prediction

2) a (polarized or unpolarized) classical beam, impinging on a beam splitter with the transmitted beam sent to Alice and the reflected beam sent to Bob.

I don't see, in your approach, how we can arrive at DIFFERENT predictions for the cases 1) and 2).

cheers,
Patrick.

 

[Sherlock]

Thanks for the corrections on details, some
comments below:

... it is not correct when you shine unpolarized light
onto a beam splitter and look at the two outcoming beams
(which DO have identical polarization at each instant of
course because being a split beam). When you perform this
experiment, you find rates which are INDEPENDENT of theta
(as well, independent rates individually, as coincident).

We wouldn't use a beamsplitter as the source, since we
wouldn't get coincidental detections this way. Would we?

When the angle p_b is such that it is perpendicular to this
direction (L), NO counts are seen at B, so no coincidences are observed.

cd_AB only goes to 0 when p_a = MDR_a = MDR_b (with dr_a = dr_b
for corresponding p_a and p_b, and ranging from some maximum
count, mdr_a = mdr_b, to a minimum of 0.

If you offset L from p_a by some angle < pi/2 (and it has
to be < pi/2 because detection at A initiates the coincidence
intervals), then moving p_b through a 90 degree rotation away
from alignment with p_a, then p_b is never perpendicular to L.

So, if L is offset from p_a, then cd_AB never reaches the
max cd_AB (which it would if p_a was aligned
with L), and cd_AB never reaches 0 because when
p_b and p_a are perpendicular there will still be >0 probability
of detection at A and >0 probability of detection at B.
So we can see how the upper and lower limits of the range of
cd_AB are determined by how much L is offset from p_a.

... for a randomly polarized beam (no L anymore) and a given p_a,
you will again find another function of theta. This time, however, by
symmetry, for a different value of p_a (but the same "kind" of random
polarization), you will find the same function of theta.

Ok, and there is a case where fixed polarization duplicates
the curve for random (entangled) polarization -- namely, when
p_a = MDR_a = MDR_b where dr_a and dr_b vary from
mdr_a = mdr_b to 0.

However, that function of theta doesn't have to be the one
you found for a polarized source.

But it happens that it is the same function that we get
for a special case of a fixed source, using the
same formulation for fixed and random (entangled) setups.

(Question: since that special case of a fixed source
seems to violate a Bell inequality, and since violation
of Bell inequalities is sort of a rough entanglement
witness, then can we say that in the special case
of fixed source the results are entangled? According
to the usual ways of evaluating entanglement the
answer would seem to be no -- but, according to my,
admittedly hurried, calculation you do get a violation
-- following the CHSH method. I don't know how to think
about this -- maybe I just did it wrong.)

... {the source polarization is relevant} in the derivation of cd_AB.

The relationship between L and p_a affects
the range of cd_AB for a fixed source.
But once we have set p_a, then the values
we get within the range determined by |L - p_a|
are completely determined by changes in
|p_b - p_a|.

The *variability* of cd_AB *within a given range*
is independent of the source polarization.

In the random entangled setup the source
polarization wrt a given coincidence interval
is unknown. But the range of cd_AB wrt a set
of runs is constant.

Again, explain me the difference between:
1) the production of entangled states (which do give us a cos^2(p_a - p_b) dependence,
but that's a pure quantum prediction
2) a (polarized or unpolarized) classical beam, impinging on a beam splitter with the
transmitted beam sent to Alice and the reflected beam sent to Bob.
I don't see, in your approach, how we can arrive at DIFFERENT predictions for
the cases 1) and 2).

It wouldn't be applied to case 2). Beamsplitters (as the
single emitter between A and B) don't produce coincidental
photon detections (p_a and p_b wouldn't be analyzing the same
thing during a coincidence interval). The approach applies to setups
where crossed linear polarizers are analyzing light from a single
emitter -- setups where it might be said that p_a and p_b are analyzing
related or the same rotational properties of the incident light during
a given coincidence interval.

Anyway, I agree with you that modeling randomly
polarized entangled light in terms of a common source polarization,
L, seems impossible using extant geometric models of the emitted
light. (I've got some ideas on how this might be done without
the usual contradictions, but must take some time to explore them.)

But, have we not shown that (1) the cd_AB for the entangled
setup can be put into the form of the product of the
individual probabilities at A and B, corresponding to a
special case of the fixed setup, (2) that the global
variable affecting *range* of coincidental detection is
|Lambda - p_a|, and (3) that the global variable affecting
*rate* of coincidental detection within a given range is
|p_a - p_b|? (Note that p_a is the convention for the
polariizer setting at the end that initiates any, ie. all,
coincidence interval(s).)

There's nothing new here, just laying some groundwork.
And, thanks again for taking the time to talk through some
of this stuff. After reading up a bit on entanglement I'm
quite sure that I understand it much less than I thought
I did when I first jumped into this thread. :)

 

[vanesch]

We wouldn't use a beamsplitter as the source, since we
wouldn't get coincidental detections this way. Would we?

That's true (except for coincidental double events at high enough rates and slow enough detectors) of course, using a QUANTUM DESCRIPTION, but my point was: how is this situation with a beamsplitter different, semiclassically, from the "entangled photon pair" situation ? There is no difference in description if you use the Maxwellian description: you have IDENTICAL beams, with identical temporal evolution of the electric field vectors in the two beams. Identical polarizations, identical amplitudes as a function of time...
So as long as you stick to a semiclassical description to explain entangled pairs, you're supposed to find exactly the same results as with a beam splitter, no ? And once you admit that there's a DIFFERENCE (which there is, according to QM and which there is, experimentally), then you cannot place yourself anymore in a semiclassical frame to do the explaining, because it is hard to find out how to find two different explanations for the same beam descriptions :-)

What I calculated (the eff^2/8 (2 - cos 2 theta) ) was in fact using the "identical classical beams" and the assumption of a "square law detector": that is, a detector that has an independent probability of clicking per unit of time, proportional to the incident Maxwellian intensity.

cheers,
Patrick.

 

[Sherlock]

That's true (except for coincidental double events at high enough rates and slow enough detectors) of course, using a QUANTUM DESCRIPTION, but my point was: how is this situation with a beamsplitter different, semiclassically, from the "entangled photon pair" situation ? There is no difference in description if you use the Maxwellian description: you have IDENTICAL beams, with identical temporal evolution of the electric field vectors in the two beams. Identical polarizations, identical amplitudes as a function of time...
So as long as you stick to a semiclassical description to explain entangled pairs, you're supposed to find exactly the same results as with a beam splitter, no ? And once you admit that there's a DIFFERENCE (which there is, according to QM and which there is, experimentally), then you cannot place yourself anymore in a semiclassical frame to do the explaining, because it is hard to find out how to find two different explanations for the same beam descriptions :-)

Yes, actually you've persuaded me a while back to drop a
semiclassical approach to understanding (quantum) entanglement. :)

 

[vanesch]

Yes, actually you've persuaded me a while back to drop a
semiclassical approach to understanding (quantum) entanglement. :)

I have to say I feel a bit burned out on the subject for the moment...

cheers,
Patrick.

 

[daytripper]

hello

Hello everyone. As you might have noticed by now, I'm daytripper. I started this thread last year when the subject matter was way over my head only to come back to see 158 replies. I'm pretty proud that I stirred up so much discussion on entanglement. Anyway, thank you all for entertaining my questions even if I don't take out time to read all 158 replies.