Polarization states directly measured : What did this experiment do?

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Polarization states "directly measured": What did this experiment do?

I ran across, on phys.org, this fairly pop-sciencey RIT press release:
http://www.rochester.edu/news/show.php?id=5692

It describes an experiment which sounds very interesting, but the way the experiment is described is colloquial and in general I do not trust university PR departments. I was wondering if someone could either explain the experiment or help me find a more hard-science source. The paper is in Nature Photonics according to the press release but I can't seem to find it listed in the current issue on their website.

The press release describes "a recently developed technique to directly measure for the first time the polarization states of light", with applications to quantum computing. Reading this, they seem to be saying they measured two conjugate variables simultaneously, i.e., both the magnetic and the electric components of a photon's polarization at once. The article suggests this particular measurement was not previously possible (what is it you normally measure when measuring polarization-- angle?).

They then go one step further though. They say they directly measured the "wavefunction" (of what?) and claim that previously, this particular measurement would have been considered not just impossible in current practice but rather impossible in theory due to the Heisenberg uncertainty principle. They describe their process as "getting around" the Heisenberg uncertainty principle. Here is the clearest statement of this I find in the press release:

"The key to characterizing any quantum system is gathering information about conjugate variables," said co-author Jonathan Leach, who is now a lecturer at Heriot-Watt University, UK. "The reason it wasn't thought possible to measure two conjugate variables directly was because measuring one would destroy the wavefunction before the other one could be measured."
Now, my amateur's understanding is that the uncertainty principle does *not* say you cannot measure two conjugate variables, but rather only that there is a accuracy lower bound on measuring any particular system of conjugate variables. Moreover, when they describe what they actually did, it seems consistent with the idea that both variables were measured but neither perfectly. They describe their technique as taking several "weak" measurements of one variable, followed by a "strong" measurement of another variable (are these technical or colloquial terms?). This seems consistent with the possibility that each "weak" measurement of A fuzzed the value of B slightly, such that both were eventually measured but both with some amount of uncertainty. So this seems to me quite consistent with the HUP. However, Prof. Leach as quoted by RIT PR above says the HUP previously ruled [whatever they did] impossible.

So here is what I wonder:

- What exactly did they measure? Am I correct that they measured the E and M components of a single photon at once? What would it even mean to "measure a wavefunction"?

- Did they actually violate the conventional understanding of the Heisenberg Uncertainty Principle in doing this? Before the technique was outlined/tried, would anyone have actually claimed that the HUP excluded this measurement?

- If they are within the Heisenberg Uncertainty Principle's bounds, it seems this means that in order to get the level of accuracy they did they must have had a trade-off where they get some certainty on these two variables but sacrifice certainty somewhere else. Correct? Where then do they make this uncertainty sacrifice?
 
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(what is it you normally measure when measuring polarization-- angle?).
You can precisely measure polarization angles if you have many photons - this is just like a classical measurement.
With a single photon, you can measure polarization along a single axis - you can decide which axis, but the result is just "yes" or "no", not an angle.

"Weak measurements" have a specific meaning in quantum physics - you get some information, but not everything.

However, Prof. Leach as quoted by RIT PR above says the HUP previously ruled [whatever they did] impossible.
No. Actually, the HUP is a statement about quantum states, and not measurements of them. It can be derived from the fundamental basics of quantum mechanics, so every violation would be a real problem.

If they are within the Heisenberg Uncertainty Principle's bounds, it seems this means that in order to get the level of accuracy they did they must have had a trade-off where they get some certainty on these two variables but sacrifice certainty somewhere else. Correct?
I think so.

rochester.edu said:
This process is repeated several times to build up accurate statistics.
=> they cannot determine the angle of a single photon (precisely). I think they just get more information than classical polarization measurements.
 

Bill_K

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Paraphrasing from http://arxiv.org/abs/1208.0034:
The HUP reads ΔA ΔB ≥ ½ |<[A, B]>|, and is uncontroversial. Heisenberg's original "measurement disturbance relationship" (MDR) would read ε(A) η(B) ≥ ½ |<[A, B]>|, where ε(A) is the measurement precision of A and η(B) is the induced disturbance of B, and is incorrect.

Ozawa proved that the correct form of the MDR is ε(A) η(B) + ε(A) ΔB + η(B) ΔA ≥ ½ |<[A, B]>|. Due to the two additional terms on the left-hand side, this inequality may be satisfied even when Heisenberg's MDR is violated.
 
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So here is what I wonder:

- What exactly did they measure? Am I correct that they measured the E and M components of a single photon at once? What would it even mean to "measure a wavefunction"?

- Did they actually violate the conventional understanding of the Heisenberg Uncertainty Principle in doing this? Before the technique was outlined/tried, would anyone have actually claimed that the HUP excluded this measurement?

- If they are within the Heisenberg Uncertainty Principle's bounds, it seems this means that in order to get the level of accuracy they did they must have had a trade-off where they get some certainty on these two variables but sacrifice certainty somewhere else. Correct? Where then do they make this uncertainty sacrifice?
Weak measurements indicate the observer does not ipso facto cause the collapse of the wavefunction. Small measurements can be taken without disturbing the wavefunction if done delicately enough contradicting some panpsychic explanations of the collapse of the wavefunction and suggesting indeterminacy can be elevated to the status of a natural law instead of remaining merely a principle. Since indeterminacy is contextual it means the first quintessential metaphor may soon be elevated to the status of a natural law.

That might sound bizarre, but to others it is no more so than using a void such as zero to balance your bank account.
 
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So if the authors aren't doing measurements, what are they doing?


mfb said:
No. Actually, the HUP is a statement about quantum states, and not measurements of them.


?

How would you know the properties of particles(e.g. position and momentum) without measuring them? Do you have a reference?



Coin said:
Now, my amateur's understanding is that the uncertainty principle does *not* say you cannot measure two conjugate variables, but rather only that there is a accuracy lower bound on measuring any particular system of conjugate variables.

Weak measurements are a controversial topic and are not accepted by everyone because if taken at face value, they would allow to circumvent the HUP and render quantum theory null and void(if there exist exceptions to the rule, the rule is wrong). This isn't a settled question so you'll get mostly opinions on this.
 

Bill_K

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Do you have a reference?
Given a reference, what would you do with it? You've ignored all the comments and references given so far.
 
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How would you know the properties of particles(e.g. position and momentum) without measuring them? Do you have a reference?
As I said, the HUP is not about measuring. The state itself has this intrinsic uncertainty. See Bill_K's link for details.

Here is an easy way to see this: Prepare a very large number of hydrogen atoms in the ground state.
For 50% of them, measure the position very precisely. Calculate the standard deviation in your sample.
For the other 50% of them, measure the momentum very precisely. Calculate the standard deviation in your sample.
The product of both will satisfy the HUP. And this is true for EVERY quantum state.

Weak measurements are a controversial topic and are not accepted by everyone because if taken at face value, they would allow to circumvent the HUP and render quantum theory null and void
No. Again, see Bill_K's reference for details.
 
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Given a reference, what would you do with it? You've ignored all the comments and references given so far.


Sorry, i didn't know only one version of the HUP failed the weak measurement test. I was too quick to dismiss both 'interpretations'. :redface:




mfb said:
As I said, the HUP is not about measuring.

And disturbing the system being measured but about what can be known about the system, right?

So the experiment and the conclusion cited in the opening post are wrong?

"In this experiment, Boyd and his colleagues passed polarized light through two crystals of differing thicknesses: the first, a very thin crystal that "weakly" measures the horizontal and vertical polarization state; the second, a much thicker crystal that "strongly" measures the diagonal and anti-diagonal polarization state. As the first measurement was performed weakly, the system is not significantly disturbed, and therefore, information gained from the second measurement was still valid. This process is repeated several times to build up accurate statistics. Putting all of this together gives a full, direct characterization of the polarization states of the light. "
 
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It is not wrong in that part, but it might be a bit misleading. With many photons, you can use a classical analysis as well. I did not find the original paper, so maybe there is something more into it.
 
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It is not wrong in that part, but it might be a bit misleading. With many photons, you can use a classical analysis as well. I did not find the original paper, so maybe there is something more into it.

It might be misleading in the part that implies that they gained information but it was an averaged out information that results from multiple measurements. So it seems the position of the particle they would get would be in the form "mostly here" and not a sharp position as the articleseems to imply and no real violation of the HUP takes place. This is hardly evidence where the particle is, it's where the particles mostly is(will be), but there is a difference right? It doesn't even seem like this is a measurement at all but a predictive value(expectation values) that may or may not be true but provides some more information(statistics) on top of a subsequent strong measurement.
 
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DrChinese

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I did not find the original paper, so maybe there is something more into it.
http://arxiv.org/abs/1206.2618

Full characterisation of polarisation states of light via direct measurement

Jeff Z. Salvail, Megan Agnew, Allan S. Johnson, Eliot Bolduc, Jonathan Leach, Robert W. Boyd
(Submitted on 12 Jun 2012 (v1), last revised 1 Aug 2012 (this version, v2))

"Ascertaining the physical state of a system is vital in order to understand and predict its behaviour. Tomography is a standard approach used to determine the form of an unknown state. Here we show that an alternative approach, based on sequential weak and strong measurements, can be used to determine the density matrix in a simple, fast, and general style. We directly measure the probability amplitudes of a variety of pure polarisation states of light. We then generalise this experiment to directly measure the Dirac distribution and consequently determine the density matrix. Our work is the first to demonstrate the direct measurement of the full description of the state of a two-dimensional system, and it has applications to measurements in foundational quantum mechanics, quantum information, and physical chemistry. "
 
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DrChinese, is a weak measurement followed by a strong measurement a violation of the HUP given that an expectation value of say momentum(averaged values of many weak measurements, statistics) is gained on top of a perfectly defined and measured position of a particle?
 

Cthugha

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http://arxiv.org/abs/1206.2618

Full characterisation of polarisation states of light via direct measurement

Jeff Z. Salvail, Megan Agnew, Allan S. Johnson, Eliot Bolduc, Jonathan Leach, Robert W. Boyd
(Submitted on 12 Jun 2012 (v1), last revised 1 Aug 2012 (this version, v2))
Just to add to that, the paper has been peer reviewed and published online yesterday in Nature Photonics: http://www.nature.com/nphoton/journal/vaop/ncurrent/abs/nphoton.2013.24.html.

This is hardly evidence where the particle is, it's where the particles mostly is(will be), but there is a difference right? It doesn't even seem like this is a measurement at all but a predictive value(expectation values) that may or may not be true but provides some more information(statistics) on top of a subsequent strong measurement.
Well, the HUP is about expectation values. It does not tell you something about what you get in a single measurement.
 
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Well, the HUP is about expectation values. It does not tell you something about what you get in a single measurement.


The experiment is done via 2 measurements - one weak and one 'strong':

"The direct measurement technique employs a "trick" to measure the first property in such a way that the system is not disturbed significantly and information about the second property can still be obtained.? This careful measurement relies on the "weak measurement" of the first property followed by a "strong measurement" of the second property."
The question was on the addition of predictive information on top of the sharply defined value after a real measurement(or at least as far as i am able to tell).
 

Cthugha

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The experiment is done via 2 measurements - one weak and one 'strong':
Ok, I should have been clearer. The HUP is not about what you get in a single measurement run. It is not about two single measurements of different polarizations or of position and momentum on one prepared particle, but it says something about the standard deviations you get when you perform the experiment very often.

Therefore the results you get using weak measurements are not too surprising. I think the whole field of weak measurements is somewhat overhyped.
 
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The point of the experiment seems different imo. The article doesn't say how many measurements were performed so i assume it wasn't just one as it would be meaningless. Assuming many number of measurements(both weak and strong) were taken, wouldn't this be new additional information(statistical) to what is available by the uncertainty relationship and the strong measurements?

BTW, the way the HUP is interpreted these days - as a limit to the certainty that we humans(no other can?) can have about an object's properties(p and x) indicates that there exists a connection between knowledge of reality and the reality out there(or at least its constituents).
 
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Cthugha

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Assuming many number of measurements(both weak and strong) were taken, wouldn't this be new additional information(statistical) to what is available by the uncertainty relationship and the strong measurements?
The result you get is the density matrix of the system (or an equivalent quasiprobability distribution). Nothing about the HUP prevents you from getting the density matrix and it has been determined for many different states.

In my opinion the merit of the manuscript is rather that it introduces an alternative to quantum state tomography when trying to find the density matrix. Quantum state tomography may become computationally intense for large and complicated systems and the technique presented here might provide a way to circumvent the computationally complicated maximum likelihood estimation step needed for tomography.
 

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