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The Analogue of Hilbert Space Is a Map of Quantum Entanglements
This is the instantaneous representation of the possib branches of quantum history. And in a sense, it's a map of entanglements. Because every one of these branchings that the fact that they had a common ancestor and that they were is a story of entanglement. We don't yet know fully how that works for quantum field theory quantu mechanics. But we can essentially compile a standard quantum circuit into a multiway graph.