Quantum Measurement: Collapse, Reduction, Decoherence, Weak & Strong Projection

[ahmad2l]

what is differences between collapse,reduction, decoherence , weak projection and strong projection in quantum measurement theories?

 

[Simon Bridge]

They are different words for describing different ideas about QM.
i.e. "collapse" refers to the way the wavefunction changes once a measurement has been made.
Looking up the definitions of the terms should give you a good idea. What did you find?

 

[naima]

According to Schrödinger the state vector evolves with time and collapse is a jump to another temporal curve.
I never found a corresponding description in Heisenberg picture.
operators jump? with given amplitudes?

 

[ahmad2l]

They are different words for describing different ideas about QM.
i.e. "collapse" refers to the way the wavefunction changes once a measurement has been made.
Looking up the definitions of the terms should give you a good idea. What did you find?

I think so.words of "collapse" and "reduction" are used in Dirac and Born interpretation of QM
and "decoherence" is used in von Neumann's measurement theory that is based on density matrix. in Dirac interpretation there is a border between quantum and classical worlds and interaction between these two worlds causes "reduction" but in von Neumann there isn't any border between quantum and classical worlds and consciousness observer causes off-diagonal components of density matrix vanish.
I think for these details, different words used for different theories.

 

[Simon Bridge]

So you already knew the answer - well done!

 

[StarsRuler]

I only speak about collapse and decoherence. I don´t know the meaning of the other terms. Collapse is when you complete the measurement about an observable and you get a measure. At the measurement moment, the wavefunction evolves instanly (really during measurement process duration) non unitarily (and then no trough Scrhödinger equation) to an eigenfunction of the measured observable with eigenvalue the result of the measure. Specifically a state with cero values in the scalar product with states non compatible with the measured result, and the sames values with the others (unless normalized)

Decoherence is for example the evolution from a pure state of the type $c_{1}|\Psi>_{1}+c_{2}|\Psi>_{2}$ (maybe with more vectors the sum) to a density matrix $|c_1|^{2}| |\Psi>_{1}<\Psi_{1}|+|c_2|^{2}| |\Psi>_{2}<\Psi_{1}|$

 

[kith]

According to Schrödinger the state vector evolves with time and collapse is a jump to another temporal curve. I never found a corresponding description in Heisenberg picture.

In the Schrödinger picture, a time dependent state ket gets projected onto a time independent eigenket of the observable. In the Heisenberg picture, this time (in)dependency is reversed.

 

[naima]

I agree with that.
At time t = 0 suppose i find that an obervable O1 has a given value. time goes from 0 to t, O1 (0) evolves to O1 (t) and i make another mesurement. Can i avoid to return to Schrödinger point of view to find the probabilities for each eigenvalues of O2?

 

[StarsRuler]

So you already knew the answer - well done!

No, it didn´t know the answer, it is a typical situation people asking on a forum not know the answers to them. And it is typical too that people that write is to answer it. Maybe you could try it sometime, Simon.

 

[DrChinese]

No, it didn´t know the answer, it is a typical situation people asking on a forum not know the answers to them. And it is typical too that people that write is to answer it. Maybe you could try it sometime, Simon.

Not sure what this is about, StarsRuler. Simon did answer. Maybe you didn't notice he is a very prolific responder.

-DrC

 

[Simon Bridge]

No, it didn't know the answer, it is a typical situation people asking on a forum not know the answers to them.

On the contrary, it is very common that people pose questions when they do know the answer - they may not realize they knew all along or lack confidence in their knowledge and just need help making the connection.

The question posed by ahmad2l in post #1 was answered in post #4 by ahmad2l ... indicating that a quoted passage confirmed something already known... ahmad was careful to cite the author of that passage correctly.

And it is typical too that people that write is to answer it. Maybe you could try it sometime, Simon.

...please read post #2 (above) and check the author credit. Thank you.

I find it is important to read the all the replies in a thread carefully, especially when I read something that appears surprising... particularly when the person posting has a different first language to me.

Aside: in many cultures it is considered rude to refer to a person as an "it".
Since gender is largely irrelevant, you may prefer to avoid "he" and "she" etc in favor of just writing the poster's handle or, maybe, a gender-neutral abbreviation like "OP".

 

[ahmad2l]

Thank you gentlemen, I almost knew the answer, but I was a bit confused when I read :
http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics
and
http://books.google.com/books/about/Foundations_of_Quantum_Mechanics_an_Empi.html?id=KjFKZTodbEIC


In this book again for "decoherence" and "reduction", new words selected:weak projection and strong projection

I think the interpretation of Bohr and Dirac and ...was incomplete and was completed by von Neumann because they did not distinguish between pure and mixed state

Von Neumann said the measurement is the reduction of the pure state to mixture ,that means quantum prababilites reduced to classical.this is called weak projection

strong projection means :reduction of classical probabilites to an eigenvector

therefore:

(transition from pure state to mixed state) according to von Neumann = (decoherence) according to von Neumann = weak projection

{(transition from pure state to mixed state) +(transition from mixed state to eigenvector)} according to von Neumann=strong projection according to von Neumann= collapse or reduction of state vector according to Bohr and others

 

[kith]

At time t = 0 suppose i find that an obervable O1 has a given value. time goes from 0 to t, O1 (0) evolves to O1 (t) and i make another mesurement. Can i avoid to return to Schrödinger point of view to find the probabilities for each eigenvalues of O2?

Yes, simply use the time-dependent eigenstates (of O2) I talked about in my previous post.