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I understand the entanglement of a pair of particles which known to show three kinds of correlation - (consider the property entangled is spin)

  1. Anti correlation - when two particles are measured in same angle They always have opposite outcome.

  2. Statistical correlation of SQUARE of sin((A-B)/2) when two particles are measured at angles A and B.

  3. Statistical correlation of 50/50 when one particle is measured numerous times at any specific angle.

How is entanglement of say 4 particle, described in terms of correlations? Can an odd number of particles get entangled too, or it has to be always an even number?

I know about mathematical superposition. What I am looking for is can it be described in terms of correlations in a similar way as the pair entanglement is described above?, or it is too complex to describe it like that and must use mathematical equations to even describe what the measurement results are going to look like.

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    $\begingroup$ There are entangled states with the statistics you describe. There are other entangled states (for two particles) with other statistics. If you want to know the statistics associated with a three or four particle state, you have to first specify which state you're talking about. $\endgroup$
    – WillO
    Jul 30, 2016 at 22:33
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    $\begingroup$ based on your response, I'd say the first thing you have to do is learn what a quantum state is. $\endgroup$
    – WillO
    Jul 30, 2016 at 23:07
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    $\begingroup$ @WillO: OK, I agree spin is a property, not a state. Irrespective of that, can the 4 particle entanglement be described in terms of statistics in a similar way a pair entanglement is? $\endgroup$
    – kpv
    Jul 30, 2016 at 23:14
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    $\begingroup$ yes more than 2 entities might be entangled. Zeilinger published about 3, Einstein about billions ( B-E condensates ). Pairs are interesting because it is easiest to highlight the entanglement, the difference with the classical statistic being maximum $\endgroup$
    – user46925
    Jul 30, 2016 at 23:40
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    $\begingroup$ @kpv: You ask if a 4 particle entanglement can be described in terms of statistics in a similar way to a pair entanglement: Answer: Of course the state cannot be described in terms of statistics, for either a four particle state OR a two particle state. You can derive the statistics from the state, but the state contains more information than just those statistics. $\endgroup$
    – WillO
    Jul 31, 2016 at 3:36

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Yours seems to be an odd way of defining entanglement. A simple guideline I use is that a state of 2 particles is entangled if you can't separate the total state into a product state of the two individual particles. Entanglement of more particles follows naturally from this guideline, as not being able to separate out any of the three individual particle states from each other.

Of course if you want to get specific you can find numerous ways of quantizing entanglement, for example by looking at the Schmidt decomposition of the state. In this case the question generally switches from "are these particles entangled" to "how much entanglement is there in this system".

An odd number of particles can definitely be entangled. In fact, you can have entangled states that don't even have a definite particle number.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – David Z
    Aug 2, 2016 at 6:58

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