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In quantum information and quantum computation, we generally use Bell type states which are maximally entangled. I find that the set of entangled states as interesting objects from a mathematical point of view and one can ask many questions regarding their structure and so on. But my question is, what are the practical uses of such states and why are they physically interesting.

The only case I can find out is, when due to some environmental interaction such states are created. However I can only see the use of maximally entangled states in literature. Caveat: In multipartite cases, maximal entanglement can be tricky.

I am not sure, whether I have have phrased the question correctly. Feel free to ask and edit. Advanced thanks for any help, suggestion etc.

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Almost all states in the Hilbert space - states that Nature may take - are non-maximally entangled states. So their "use" is everywhere. Nothing in Nature would really work if there weren't non-maximally entangled states. Every correlation of systems in the quantum regime means that the systems are entangled.

Unentangled states are a measure zero set, and so are maximally entangled stats. Despite their being measure zero sets, they're often discussed, too. Maximally entangled states are often discussed in quantum information because they maximize entanglement – and entanglement itself is something that is useful or that people want to demonstrate – and because quantum computers etc. often deal with very simple states and the maximally entangled states belong to this class, too.

Entangled states are also "used" to emphasize the differences between quantum physics and classical physics i.e. the "non-intuitive" character of quantum mechanics.

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People often forget that one of the earliest proposed applications of quantum information theory, quantum key distribution via the BB84 protocol, involves no entanglement whatsoever — only product states and classical information are ever transmitted between Alice and Bob.

This goes to show that if you think anything in quantum mechanics is particularly interesting, you might want to consider it interesting that there are any pure states whatsoever beyond the standard basis — a fact without which entanglement wouldn't exist anyway.

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A trend in Quantum Information is to regard entanglement as a resource. In particular, entangled states are a resource for a number of protocols which are impossible in classical theory, e.g., teleportation, dense coding, secret sharing, etc... It turns out that given certain restrictions on what kind of physical operations one can perform (say, physically separated at points A and B), entanglement between A and B can only decrease. However, in doing so, it may assist in performing tasks that are not possible otherwise.

The celebrated entanglement distillation protocols allow to obtain few highly entangled states from many weakly entangled ones. This is the reason why people concentrate on maximally entangled ones. Beware, not all states are distillable (bound entangled states are not distillable). There is a huge zoology of entanglement measures, and lots of interesting and counterintuitive results regarding distillation of entangled states.

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Quantum teleportation and super dense coding use entanglement. You can teleport a qubit, storing A LOT of information in the coefficients $\alpha \vert0> + \beta \vert 1>$ by communication only 2 classical bits of information.

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