What information is carried by single quantum objects?

[zdcyclops]

A single electron is fired at a detector, what do we know about the electron after it reaches the detector that we did not know before.

 

[bhobba]

Assuming it's not destroyed by the detector its state may change. Such are known as filtering type observations and are synonymous with state preparation procedures. The detector outcome determines the state.

Thanks
Bill

 

[bahamagreen]

bhobba's answer, as always, is the canonical one; but I think your question may be problematic perhaps assuming that information about the electron's possible attributes exists prior to selection of an experimental setup defining the attribute to be measured and its subsequent measurement.

There are an infinite number of possible attributes to measure, virtually all of them quite impossible to prepare and experimentally setup... any idea that the electron has these attributes (is carrying answers to every possible question that could be posed to it by innumerable corresponding experimental questions made manifest by preparations and measurements) is kind of backwards... as bhoba says, "The detector outcome determines the state."

At first this seems peculiar, but if you understand Fourier it is kind of like that... a waveform may be decomposed into sine waves, but also decomposed into any other arbitrary waveform. The choice of waveform with which to perform the decomposition is like choosing the experimental preparation (the arrangement of the question to ask, the choice of attribute to measure), the resulting decomposition being like the measured attribute... the answer shows up as a result of choosing the question.

 

[Strilanc]

It depends on the experiment. What does the detector detect? Is the fired electron being prepared in a known state? A mixed state?

For example, suppose the detector records the spin of the electron along the Z axis and the electron's spin is prepared in the state $\left| \uparrow \right\rangle$. Then we don't really learn much at all about the spin by firing the electron at the detector. The detector is going to say it's upward... but we already knew the electron's spin was being prepared that way.

If we're instead preparing the electron's spin to be in the state $\frac{1}{\sqrt{2}} \left| \uparrow \right\rangle + \frac{1}{\sqrt{2}} \left| \downarrow \right\rangle$, and we have two Z-axis-spin detectors one after another. Before the electron passes the first detector we don't know what the second detector will read. But after the electron passes through the first detector, we do know what the second detector will read: whatever the first detector just output.

So that's one important thing that detectors can tell you about: information about what the next detector will say.

 

[zdcyclops]

It depends on the experiment. What does the detector detect? Is the fired electron being prepared in a known state? A mixed state?

For example, suppose the detector records the spin of the electron along the Z axis and the electron's spin is prepared in the state $\left| \uparrow \right\rangle$. Then we don't really learn much at all about the spin by firing the electron at the detector. The detector is going to say it's upward... but we already knew the electron's spin was being prepared that way.

If we're instead preparing the electron's spin to be in the state $\frac{1}{\sqrt{2}} \left| \uparrow \right\rangle + \frac{1}{\sqrt{2}} \left| \downarrow \right\rangle$, and we have two Z-axis-spin detectors one after another. Before the electron passes the first detector we don't know what the second detector will read. But after the electron passes through the first detector, we do know what the second detector will read: whatever the first detector just output.

So that's one important thing that detectors can tell you about: information about what the next detector will say.

Thanks but does not the fact that there is a change in the state of the detector tell you the location of the electron? Is this not true of all such experiments regardless of what attribute you are trying to measure? When there is a change in the detector you know where the electron is and when it arrived, and from this from this other things can be calculated.

 

[naima]

When you say that an electron carries information it looks like a local property of a particle. When you have two maximally entangled particles the information is not localized in each of them. It "stays" in their correlation. If a set of particles are weakly entangled i have no idea about how information is shared.

 

[bhobba]

When you say that an electron carries information it looks like a local property of a particle. When you have two maximally entangled particles the information is not localized in each of them.

It is 'localised' just as much as a pure state. It acts as a mixed state.

Personally I find this information thing far too wishy washy. Just about everything carries information, quantum or non quantum.

Thanks
Bill

 

[Nugatory]

When there is a change in the detector you know where the electron is and when it arrived, and from this from this other things can be calculated.

We know that the electron was in the general neighborhood of the detector and we know approximately when the state change happened. That reduces our uncertainty about the position of the electron, but it commensurately increases our uncertainty as to the momentum.

 

[naima]

Yes. Rovelli wrote that in QM the information is finite in the sense that new information may have to erase a part of previous knowledge.