Equation 7 · Part 1 · How Much of Gravitationally Induced Entanglement Is in the Eye of the Frame

Entangling phase difference

\varphi_{\text{ent}} = \varphi_{LL} + \varphi_{RR} - \varphi_{LR} - \varphi_{RL}

\varphi_{\text{ent}}

What this part means

The phase combination left after local phases of A and B cancel. It compares matching branch pairs (LL and RR) with crossed pairs (LR and RL). In an ideal balanced, pure two-branch state, its value modulo 2π determines the generated two-qubit entanglement.

Its job in the formula

This is the alternating phase difference that remains after all phases attributable to A alone or B alone cancel. In the ideal balanced state it sets the entanglement magnitude.

Full expressionEntangling phase differenceArticle meaning

The passage around this formula

…combination survives that removal: $\varphi_{\text{ent}} = \varphi_{LL} + \varphi_{RR} - \varphi_{LR} - \varphi_{RL}$ . 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 $\varphi_{\text{ent}}$ and of the locally removable phases only — never of anything else. Because $\varphi_{\text{ent}}$ is built entirely from relational branch separations, it is invariant under the same quantum-reference-frame transformations that reshuffle the entanglement structure between the…

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Learn the underlying idea

A quantum phase is an angle attached to a complex amplitude. One path’s phase can be changed by convention; phase differences between alternative paths can change interference and entanglement.

Open the illustrated quantum phase and two-path entanglement guide →

See this notation across published equations →

Sources cited in the article section

[6] On the possibility of laboratory evidence for quantum superposition of geometries ↗

These citations provide research context; check each source for the exact claim it supports.