# Degrees of entanglement?

Hi, I'm wondering what is meant by degrees of entanglement, and am looking for a simple concrete example. Here's a guess at an example, and then a more general definition based on it:
Examples of perfect entanglement would be the Bell singlet states. To use a position basis example, for two particles confined to one dimension we might have perfect entanglement:

c1(|x1>1|x10>2) + c2(|x2>1|x11>2)

Now for imperfect entanglement or "less" entanglement we might have:

c1|x1>1(c2|x10>2+c3|x11>2) + c4|x2>1(c2|x10>2+c3|x12>2)

So in this example I'm thinking that if you measure particle 1 and collapse it position x1, then you don't fully collapse particle 2; you only collapse it to a superposition of x10 and x11; similarly if you measure 1 and collapse it to x2, you don't fully collapse particle 2, you only collapse it to a superposition of x10 and x12.

So then general definition of degrees of entanglement would be "the more entangled the particles are (in basis B) the more that a collapse of one particle (in B) will lead to a more confined collapse (i.e. reducing superposition spread) of the other particle (in B).

Does my example make sense (not sure if the c#'s really work out here)?
Does the example illustrate the idea of degrees of entanglement?
Do you know of better simple illustrations of the idea?
What are some realistic illustrations of the idea?

naima
Gold Member
look at the curve in entropy
you move between two unentangled states (null entropy) and in the middle there is a Bell state (entropy = 1) which is maximally entangled.

look at the curve in entropy
you move between two unentangled states (null entropy) and in the middle there is a Bell state (entropy = 1) which is maximally entangled.

Thanks but if I could understand your link then I would have little need to ask this question. Setting aside very general complex measures (e.g. using entropy) of entanglement degrees, I would just like to see a straightforward example of imperfect entanglement. For example I'm wondering if the simple one dimensional space example I offered is an example.

kith