Understanding Pure and Mixed Quantum States in Entanglement

[daniellao]

Quick Question.
I've recently been told that a pure quantum state is the only state that can be entangled in quantum entanglement and display the results that is predicted with QM.
The mixed states would lose their superposition immediately after entanglement.
Is this true?

 

[Khashishi]

No. You are probably referring to decoherence, which happens when something gets entangled with a macroscopic environment. But its possible to have mixed entangled states on a microscopic scale.

 

[daniellao]

My confusion is derived from another thread when someone said "you seem to be saying that when two things are entangled.. they are not in superposition."
A very active member of the community responded with "That's exactly what I am saying and what my analysis showed".
This is confusing to me as I thought the whole idea of counterfactual definiteness was that entangled pairs were in a superposition prior to measurement/observation.

 

[atyy]

Mixed states can be entangled. However, there is no "standard" calculation one can do to say that a mixed state is entangled, where there is a standard calculation for pure states.

http://arxiv.org/abs/quant-ph/0109124
Mixed-state entanglement and quantum communication
Michal Horodecki, Pawel Horodecki, Ryszard Horodecki

 

[bhobba]

My confusion is derived from another thread when someone said "you seem to be saying that when two things are entangled.. they are not in superposition."

They are not in a pure state, but act like they are in a mixed state. Superpositions are basically associated with pure states. To fully understand it you need to study a good book on QM and see what happens when the Born Rule is applied to a superposition and a mixed state.

For example if the pure state is |u> = c1 |a> + c2|b> then it is in a superposition of |a> and |b> and you can get interference because c1 and c2 are complex numbers. That's quantum weirdness in full force. But if you have the mixed state p1 |a><a| + p2 |b><b| then p1 and p2 are positive numbers that add up to one. You can view it as the system being in state |a> with probability p1 and in state |b> with probability p2. Interference is not possible. If you are observing if the system is in state |a> or |b> for a pure state you can't fool yourself and say the system was in state |a> or |b> before observation. That is exactly why the world around us behaves classically - everything is entangled so are in mixed states that behave in a common-sense way without interference. The other part of the 'puzzle' is decoherence singles out a particular basis ie it singles out the |a> and |b> states of the mixed state - that does not happen for pure states that can be broken up into superpositions in all sorts of ways. Strictly speaking so can a mixed state - but decoherence singles out a preferred basis.

Don't get too worried by that thread. Normally we don't get caught up in that pure states don't really exist - its a small point really. The reason that thread went down that path is the starter wanted to know what it feels like to be a pure state - he thinks you then become unreal. The only real way to answer it is to be pedantically exact and point out they only exist as approximations for things like electrons, and most definitely do not exist for macro objects like cats.

Thanks
Bill