Can you measure a particle without breaking superposition?

  • #1

Main Question or Discussion Point

Is it possible to measure an electron, and, say, get multiple simultaneous results about it's motion, as you didn't break superposition? (E.g. you could simultaneously read 5mph, 10 mph and 15mph), and could this be used for quantum computers, to store store and gain huge amount of information in a particle in superposition?
 

Answers and Replies

  • #2
jfizzix
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The short answer is yes, but it's a tradeoff, and you don't get multiple results at the same time, but instead a single superposition.
The more information you obtain, the more the superposition is broken.

The measurement process itself is an interaction between the measured object and the measurement device, where the quantum state of the measurement device becomes correlated (or entangled) to the quantum state of the measured object.
If you make this interaction weak, the correlation is weak, and you only get a little bit of info, but the state of the object is only weakly disturbed.
If the measurement interaction is strong enough that knowing the state of the measurement device tells you as much as possible about the measured object, the disturbance to the state of the object is maximum as well.

Unfortunately, I can't comment on whether or how weak interactions would be applicable in the field of quantum computing.

You'll be interested to know what you describe falls under the field of quantum weak measurements.
https://arxiv.org/abs/1305.7154
There's some really neat things you can do in this field, such as ultra-sensitive measurements of beam-deflections less than a pico-radian in angle:
http://www.pas.rochester.edu/~jhgroup/papers/dixon-prl-09-04.pdf
For reference, a pico radian is approximately the angle subtended by a hair's width (~15 microns) over the distance from the Earth to the Moon.
The advantages also extend to ultra-sensitive displacement measurements in general (e.g. frequency shift):
http://www.pas.rochester.edu/~jhgroup/papers/starling-pra-10-12.pdf
Besides precision measurement, weak measurement techniques provide a much simpler way to directly measure the quantum wavefunction:
https://arxiv.org/abs/1112.3575
More recently, it's been shown that the interaction doesn't have to be weak to still work for this kind of quantum state measurement:
https://arxiv.org/abs/1504.06551
 
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  • #3
PeterDonis
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The short answer is yes,
I think the short answer is actually no, but the OP's question needs to be clarified first.

If you measure an observable, you get one result for that observable. So this...

you could simultaneously read 5mph, 10 mph and 15mph
...is not possible, because to "read" a speed you have to measure speed, and then you will measure a single speed, not a superposition of speeds.

If you measure some observable other than speed, then the system will end up in a state that might be describable as a superposition of different speeds. But in that measurement you will not "read" any speed at all. You will certainly not "simultaneously read" multiple speeds.
 
  • #4
hilbert2
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In addition to the weak measurements, there's a somewhat related concept of "nondemolition measurement", which means that the system does not quickly start to differ from the state it collapsed to (as would happen after a position measurement that collapses the wavefunction to a sharp Gaussian with a wide variation of momentum eigenstates in it).
 
  • #5
Is it possible to measure an electron, and, say, get multiple simultaneous results about it's motion, as you didn't break superposition?
If I make a mistake in the following, would somebody please educate me? Thank you.

I'll assume that your electron was in a pure state.

You say it's a superposition state. That means the state vector is not parallel to any of your basis vectors. The fact that you call it a superposition implies that you, or the measuring device, has already specified basis vectors.

Then, you measure it. The result must be parallel to one of the basis vectors. So, you have broken superposition.

One way to measure without breaking superposition is to select a basis vector parallel to the original state vector, and have all the other basis vectors orthogonal to it. But that's no good because (a) relative to your new basis vectors it's not in superposition, and (b) you know the answer before you make the measurement.

A more interesting way to do this is to have the electron partially entangled with something else. If you measure the something else, you will get partial information about the electron, and although that will change its state, its new state may also be a superposition.

Can you get multiple simultaneous results? I'd like to see that. What would it look like? A double-exposed photo?

You can philosophically suppose that you got multiple results, one in each of the "many worlds" that are generated by your measurement. But it's not easy to interact with those worlds. Even if you can keep them coherent, you're only going to get interference, not a printout with three results on it.

David
 
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