Entanglement with more than two particles

[Honorable_Death]

I know that if you have two entangled particles and measure ones spin, the other one must have the opposite spin, but what if you have 3 particles entangled with each other, what would happen?

 

[ZapperZ]

You may want to do a search on here. DrChinese has a thread in which he, I, and a few people pointed out 4, 5, and even up to 12 multiparticle entanglement.

Zz.

 

[slyboy]

Even two particle entanglement is a bit more interesting than your description suggests. In a maximally entangled state there is perfect correlation or ant-correlation between the particles, but other states can be entangled as well without perfect correlation or anti-correlation (in the sense of being able to violate Bell inequalities for example). In general we quantify the amount of entanglement in a state by asking how many maximally entangled states you can make if you have a large number of systems in the state and Alice and Bob can perform local operations on their halves of the states and communicate with each other classically. In the case of pure, two-particle states, this leads to an essentially unique measure of entanglement called the "entropy of entanglement".

In the case of multi-particle states, things are a lot more complicated. There are several inequivalent types of multi-particle entanglement that cannot be converted into each other by local operations and classical communication. Multi-particle states can also be used to derive very elegant proofs of Bell's theorem that don't involve inequalities.

Multi-particle entangled states are actually pretty generic in modern physics, occurring as ground states of many natural many-body Hamiltonians. However, it is only recently that people have begun to use entanglement theory to study the properties of these systems. Older treatments were all cast in terms of correlation functions, which are not completely unrelated to entanglement, but they do not clearly distinguish classical correlations from "genuinely quantum" correlations due to entanglement. In particular, entanglement studies have lead to new algorithms for simulating some of these systems on classical computers, which people did not know how to do before. This is currently a very active area of research.

 

[DrChinese]

I know that if you have two entangled particles and measure ones spin, the other one must have the opposite spin, but what if you have 3 particles entangled with each other, what would happen?

FYI: Entangled photon spin is not always anti-correlated. For instance, with Parametric Down Conversion (PDC), there is Type I and Type II. Type I photon pairs have the same polarization, and that is perpendicular (orthogonal) to the input photons. Type II photon pairs consist of one perpendicular and one parallel to the input beam.

There are a variety of ways to get multiples (>2) which are entangled. With PDC, you can get this when 2 input photons degenerate into 2 pairs within a narrow time window. This is a spontaneous result, one which occurs only occasionally. In one experiment, they got 4 entangled photons out once in 24 seconds on average.

Reference: "Experimental observation of four-photon entanglement from down-conversion".