Quick Introduction To Quantum Entanglementpic.twitter.com/9aDo9lAuNC
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In general, elements of X⨂Y are linear combinations of decomposable tensors, just like in your post.
I’m seeing what you’re saying, but I thought that a tensor product of reps can always be decomposed into a direct sum of its irreps.. or is that just SU(N)?
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You are right, but I'm not talking about irreps of SU(N) or spins or anything in particular, just quantum systems in general.
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I think I see .. but doesn’t this example (main tweet) show that this is not always true of entangled states ?
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tensor product of irreps* I mean
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Tensor product of any reps (or irreps) is still a representation, and for compact groups (e.g. SO(N), SU(N), Spin(N), finite groups) any representation decomposes into irreps. (technically I believe you need the reps to be strongly continuous, though)
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