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Equation 8 · How Much of Gravitationally Induced Entanglement Is in the Eye of the Frame

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φent\varphi_{\text{ent}}

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φent\varphi_{\text{ent}}

Symbol varphi_ent

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subscript

subscript

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and the paper’s core theorem is that both the entanglement quantifiable in the state and the actual spin-correlation witness a detector reads out are functions of φent\varphi_{\text{ent}} and of the locally removable phases only — never of anything else. Because φent\varphi_{\text{ent}} is built entirely from relational branch separations, it is invariant under the same quantum-reference-frame transformations that reshuffle the entanglement structure between the three frames. The witness, in other words, is a scalar. Every frame computes the identical number for it, even while disagreeing about which subsystems that number’s nonzero value is entanglement “between.”

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