Quick Introduction To Quantum Entanglementpic.twitter.com/9aDo9lAuNC
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From mathematician's point of view entanglement is exactly the fact that not all tensors are decomposable. It totally clicked me once I realized that.
hmm what do you mean? this is the singlet representation, an irreducible representation, of su(2) x su(2)
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I mean the following: given a system with Hilbert state X and another with Y, the joint state space is X⨂Y. A state there X & Y are independent would look like a⨂b (a decomposable tensor) for some a∊X and b∊Y, but not all elements of X⨂Y are decomposable.
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In general, elements of X⨂Y are linear combinations of decomposable tensors, just like in your post.
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This term "irreducible" is a speed-bump for me. Does it mean "there is no other rep that is a ..." what? Also, what is the cross in su(2) x su(2)? Tensor? Cartesian? Should those be SU(2)? Know a short reference on this background info? I guess it's "representation theory?"
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