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Equation 9 · Part 2 · How Much of Gravitationally Induced Entanglement Is in the Eye of the Frame

subscript

φent\varphi_{\text{ent}}
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

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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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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