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## Main Question or Discussion Point

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>

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

c1|x1>

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?

Interested in your thoughts!

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?

Interested in your thoughts!