Are analog Hawking quanta quantum entangled with their partners?
In plain words
Hawking particles should be born in pairs that are entangled, meaning linked more strongly than any classical correlation allows, with one member escaping and one falling in. Experiments so far infer this link from density measurements alone, and it is disputed whether that is enough.
Precise statement
For phonon modes $b_u$ (outgoing Hawking mode in the subsonic region) and $b_d$ (partner mode in the supersonic region) at frequency $\omega$, the Gaussian state is non-separable if $\left|\langle b_u b_d\rangle\right|^2 > n_u n_d$, with $n_u, n_d$ the mode occupations. Determine whether this inequality holds in a BEC analog black hole, by a measurement that either accesses phase as well as density quadratures or validates the Gaussian and stationarity assumptions independently, and identify the frequency range in which entanglement survives initial thermal occupation. An answer is a certified yes or no with the frequency window.
What would settle it
A quadrature-resolved or assumption-validated correlation measurement showing violation of the separability bound with stated confidence.
Status in the literature
Unverified note
Entanglement claims from density-only measurements (Steinhauer 2016 and later) rely on assumptions about the phonon state that critics, including Leonhardt (2016), dispute; Bell-inequality tests for analog Hawking pairs were proposed in theory (Ciliberto, Emig, Pavloff, Isoard, PRA 109, 063325, 2024).