Quantum Decoherence: Understanding Contradictions

[Alfrez]

Your statements are too vague to allow them to be properly discussed.



It may or may not be in a pure state. My assumption was just for simplicity.



A pure state means that the system can be described by a wave function psi, while mixed states must be described by a density matrix rho. (The density matrix can also describe pure states, namely when it is of the form rho = psi psi^*.)

This is completely independent of a discussion of phase relationships or interference.
In particular, you can observe interference only for a small system, not for a system and its environment together.




One usually assumes a system to be in a pure state when discussing superpositions and entanglement. But pure states neither need to be entangled nor be in a superposition.



Yes. A unitary dynamics preserves the pureness of a state.



No. pure state means not mixed, and nothing else.

Hi, I have thought of what you said for quite a time and read many references in the internet and elsewhere trying to refute your statement "pure states neither need to be entangled nor be in a superposition". But I found this at Wikipedia

"Applying the superposition principle to a quantum mechanical particle, the configurations of the particle are all positions, so the superpositions make a complex wave in space. The coefficients of the linear superposition are a wave which describes the particle as best as it possible, and whose amplitude interferes according to the Huygens principle"

You see, quantum mechanics always involves waves, and from the above where it was mentioned "the configurations of the particle are all positions, so the superpositions make a complex wave in space", so superpositions are automatically part of QM where waving is part of it. Now you mentioned "pure states neither need to be entangled nor be in a superposition". How can that be. Give an example of pure state where there is no quantum wave involved.

 

[A. Neumaier]

Hi, I have thought of what you said for quite a time and read many references in the internet and elsewhere trying to refute your statement "pure states neither need to be entangled nor be in a superposition". But I found this at Wikipedia

"Applying the superposition principle to a quantum mechanical particle, the configurations of the particle are all positions, so the superpositions make a complex wave in space. The coefficients of the linear superposition are a wave which describes the particle as best as it possible, and whose amplitude interferes according to the Huygens principle"

You see, quantum mechanics always involves waves, and from the above where it was mentioned "the configurations of the particle are all positions, so the superpositions make a complex wave in space", so superpositions are automatically part of QM where waving is part of it. Now you mentioned "pure states neither need to be entangled nor be in a superposition". How can that be. Give an example of pure state where there is no quantum wave involved.

''quantum wave'' is a term not used by professionals, but the use in your sources seems to be synonymous with that of pure state.

The subsystems P (particle) and E (environment) of the system P+E are unentangled = not in a superposition if the system is in the state psi_P tensor psi_E for states psi_P of the particle and psi_E of the environment. In all other cases (the usual cases) they are entangled.

I leave it to you to translate this precise statement into your fuzzy language.