What really is a Weak Measurement?

Does it explain what occur during strong measurement or "approximately" solve the measurement problem? I'm asking because below it is mentioned that "it is this uncertainty that creates the uncontrollable, irreversible disturbance associated with measurement". Does it mean that measurement problem is related to uncertainty inverse relationship between position and momentum? Can you give other example beside position, momentum where weak measurement is valid.. maybe energy-time uncertainty? Also isn't weak measurement like being a little "pregnant"?

Here's about weak measurement from Kocsis, et al paper "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer" (What is the mainstream consensus about Weak Measurement? Is it still controversial. How do you understand it? Can you give other more obvious example about it as the language used below (like "pointer shift", "single shot", etc.) is somewhat hazy to me. Thanks.):

"Weak measurements, first proposed 2 decades ago (7, 11), have recently attracted widespread attention as a powerful tool for investigating fundamental questions in quantum mechanics (12–15) and have generated excitement for their potential applications to enhancing precision measurement (16, 17). In a typical von Neumann measurement, an observable of a system is coupled to a measurement apparatus or “pointer” via its momentum. This coupling leads to an average shift in the pointer position that is proportional to the expectation value of the system observable. In a “strong” measurement, this shift is large relative to the initial uncertainty in pointer position, so that significant information is acquired in a single shot. However, this implies that the pointer momentum must be very uncertain, and it is this uncertainty that creates the uncontrollable, irreversible disturbance associated with measurement. In a “weak” measurement, the pointer shift is small and little information can be gained on a single shot; but, on the other hand, there may be arbitrarily little disturbance imparted to the system. It is possible to subsequently postselect the system on a desired final state. Postselecting on a final state allows a particular subensemble to be studied, and the mean value obtained from repeating the weak measurement many times is known as the weak value. Unlike the results of strong measurements, weak values are not constrained to lie within the eigenvalue spectrum of
the observable being measured (7). This has led to controversy over the meaning and role of weak values, but continuing research has made strides in clarifying their interpretation and demonstrating a variety of situations in which they are clearly useful (16–21)."

I wonder how this is related to decoherence. Here when a system is weakly coupled to environment, interference pattern still exist and intensity proportional to the coupling. So maybe Weak Measurement work because everything is quantum? But decoherence is not equal to collapse. It just looks like collapse. So collapse is still a mystery in addition to Decoherence and Weak Measurements.

Also I wonder if the concept of weak measurement is used only in analyzing system based merely on HUP.. like momentum, position. This means the double slit can be analyzed soley on HUP and wave is just an 'extra' factor?

Demystifier
Gold Member
You can find an explanation of weak measurements "for children" in my blog
https://www.physicsforums.com/blog.php?b=3077 [Broken]
(second comment)

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You can find an explanation of weak measurements "for children" in my blog
https://www.physicsforums.com/blog.php?b=3077 [Broken]
(second comment)

Lol... anyway you wrote the following in the blog. I was asking above if weak measurement was connected with momentum. Why is the example always about momentum. Is there weak measurement that doesn't involve momentum, how? Anyone else knows?

To understand what weak measurement is, the following analogy from everyday life is useful.

Assume that you want to measure the weight of a sheet of paper. But the problem is that your measurement apparatus (weighing scale) is not precise enough to measure the weight of such a light object such as a sheet of paper. In this sense, the measurement of a single sheet of paper is - weak.

Now you do a trick. Instead of weighing one sheet of paper, you weigh a thousand of them, which is heavy enough to see the result of weighing. Then you divide this result by 1000, and get a number which you call - weak value. Clearly, this "weak value" is nothing but the average weight of your set of thousand sheets of papers.

But still, you want to know the weight of a SINGLE sheet of paper. So does that average value helps? Well, it depends:

1) If all sheets of papers have the same weight, then the average weight is equal to weight of the single sheet, in which case you have also measured the true weight of the sheet.

2) If the sheets have only approximately equal weights, then you can say that you have at least approximately measured the weight of a single sheet.

3) But if the weights of different sheets are not even approximately equal, then you have not done anything - you still don't have a clue what is the weight of a single sheet.

But what if you don't even know whether 1), 2) or 3) is true? Then you have different interpretations of your weak measurement. And that is precisely the case with quantum mechanics: We don't know whether particles have even approximately equal velocities at the same position (with the same wave function), so we have different interpretations. Bohmian interpretation says they have exactly equal velocities, which corresponds to the case 1), while Copenhagen interpretation corresponds to the case 3).

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Demystifier
Gold Member
Lol... anyway you wrote the following in the blog. I was asking above if weak measurement was connected with momentum. Why is the example always about momentum. Is there weak measurement that doesn't involve momentum, how? Anyone else knows?
Weak measurement may be about any observable, not only momentum.

Weak measurement may be about any observable, not only momentum.

It works only on HUP partners like momentum-position, energy-time right? Because by changing one of them. The other is affected inversely. Or can weak measurement work on non HUP entities like between momentum and time?

f95toli
Gold Member
. Why is the example always about momentum. Is there weak measurement that doesn't involve momentum, how?

When we talk about position and momentum in "general terms" in QM it is usually implied that we are talking about generalized position and momentum. "Generalized" here refers to the way they are used in the Lagrangian. Hence, any variable that for example takes the place of momentum in a Lagrangian can be thought of as being a "generalized" momentum.

My favourite example is charge and phase, which are the generalized momentum and position for electrical circuits. A lot of the work on weak measurements (both theoretical and experimental) have been done on electrical circuits (such as superconducting qubits), so I'd say if is actually quite common for the weak measurements to be done on systems where we are not dealing with momentum in the usual meaning of the word.

Demystifier
Gold Member
It works only on HUP partners like momentum-position, energy-time right?
Wrong.

Or can weak measurement work on non HUP entities like between momentum and time?
Yes (provided that you know how to define the time operator).

Does it explain what occur during strong measurement or "approximately" solve the measurement problem? I'm asking because below it is mentioned that "it is this uncertainty that creates the uncontrollable, irreversible disturbance associated with measurement". Does it mean that measurement problem is related to uncertainty inverse relationship between position and momentum? Can you give other example beside position, momentum where weak measurement is valid.. maybe energy-time uncertainty? Also isn't weak measurement like being a little "pregnant"?

Here's about weak measurement from Kocsis, et al paper "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer" (What is the mainstream consensus about Weak Measurement? Is it still controversial. How do you understand it? Can you give other more obvious example about it as the language used below (like "pointer shift", "single shot", etc.) is somewhat hazy to me. Thanks.):

"Weak measurements, first proposed 2 decades ago (7, 11), have recently attracted widespread attention as a powerful tool for investigating fundamental questions in quantum mechanics (12–15) and have generated excitement for their potential applications to enhancing precision measurement (16, 17). In a typical von Neumann measurement, an observable of a system is coupled to a measurement apparatus or “pointer” via its momentum. This coupling leads to an average shift in the pointer position that is proportional to the expectation value of the system observable. In a “strong” measurement, this shift is large relative to the initial uncertainty in pointer position, so that significant information is acquired in a single shot. However, this implies that the pointer momentum must be very uncertain, and it is this uncertainty that creates the uncontrollable, irreversible disturbance associated with measurement. In a “weak” measurement, the pointer shift is small and little information can be gained on a single shot; but, on the other hand, there may be arbitrarily little disturbance imparted to the system. It is possible to subsequently postselect the system on a desired final state. Postselecting on a final state allows a particular subensemble to be studied, and the mean value obtained from repeating the weak measurement many times is known as the weak value. Unlike the results of strong measurements, weak values are not constrained to lie within the eigenvalue spectrum of
the observable being measured (7). This has led to controversy over the meaning and role of weak values, but continuing research has made strides in clarifying their interpretation and demonstrating a variety of situations in which they are clearly useful (16–21)."

Does the existence of weak measurement also suggest that FTL transmission of "weak/partial/semi-reliable" information is possible?

I have a feeling that:

weak measurement, de Broglie-Bohm, DCQE, Coincidence counter --- are closely linked and there is an answer/understanding hidden there that explains why FLT is not possible.

That understanding will also answer if randomness is inherent or not.

Wrong.

Yes (provided that you know how to define the time operator).

Ok. But Weak Measurement seems to have its esoteric terms. Even in wiki entry on it says thus:

"After the measurement the measuring device pointer is shifted by what is called the "weak value". So that a pointer initially pointing at zero before the measurement would point at the weak value after the measurement. The system is not disturbed by the measurement"

Now let's say I want to apply this by putting a calcite in a tiny portion of say the right slit. Now I want to perform weak measurement such that if the photon passes thru the right slit, I can only detect 0.0001% of its passage. Would this constitute a weak measurement? You may say not because there mere detection of 0.0001% determines which slit the photon passes. But it's still weak measurement, isn't it?