**Quantum motivation**

The key insight used in the current generation of quantum astrometry is the exploitation of entanglement to perform interferometry from astrophysical sources. The current generation of experiment focuses on the usage of Bell pairs to perform this interferometry, as has been detailed in [1]. These techniques have a robust basis in quantum optics in for example the tabletop setting, and therefore should be portable to astrophysical applications in principle.

There are at least two ways of generalizing this approach that would be interesting to study to broaden the scope of this experiment. First, there are many simple patterns of entanglement of small numbers of qubits beyond Bell pairs; simple three qubit examples include the GHZ state (|000>+|111>) and the W state (|100>+|010>+|001>), along with their natural generalizations to larger numbers of qubits. In the quantum optics community, studies of interferometry leveraging such entanglement has already been performed; see for example [2] for a relevant review of progress in this direction. Repeating the analysis of [1] using these more novel forms of entanglement could provide yet greater enhancements to the precision and robustness of the astrometric measurements. Indeed, certain entanglement patterns may prove useful for precise measurements of certain astrophysical quantities, resulting in a conceptually pleasing scenario where the measurement desired determines the simple entangled state used.

To perform this generalization, one would have to better understand the structure of multipartite entangled states. This is essential to the determination of which states would be “interesting” from an interferometric perspective, in terms of both robustness against decoherence and precision properties. Therefore, a parallel study of entanglement measures for diagnosing the type of multipartite entanglement when given a copy quantum state is also needed, to aid in the selection of the optimal multipartite entangled states for astrometry. Once the optimal states have been ascertained, it will be necessary to demonstrate on a small experiment that they, indeed, possess the desired properties on the tabletop before porting the experiment to observatories.

The second generalization of this approach is to use quantum astrometry to study Bell inequality violation in the cosmic microwave background. It has been proposed in [3] that the CMB is an interesting arena to search for violations of Bell’s inequalities. Such violations would indicate that the CMB has an intrinsically quantum mechanical nature, and that its correlations cannot be explained by classical physics alone. The quantum astrometry techniques developed thus far seem well-suited for generalization to study such questions, with some simple modifications to their experimental design. Again, a proof of principle version of this experiment leveraging tabletop and kilometer-scale versions of Bell inequality experiments such as those in [4] adapted to the interferometric setup would be essential before porting the strategy over to observatories.

1. Two-photon amplitude interferometry for precision astrometry, P.Stankus, A.Nomerotski, A.Slosar and S.Vintskevich, arxiv:2010.09100.

2. Multiphoton entanglement and interferometry, Jian-Wei Pan, Zeng-Bing Chen, Chao-Yang Lu, Harald Weinfurter, Anton Zeilinger, and Marek Żukowski, Rev. Mod. Phys. 84, 777 – Published 11 May 2012.

3. A model with cosmological Bell inequalities, Juan Maldacena(Princeton, Inst. Advanced Study), Fortsch.Phys. 64, 2016.

4. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres, B. Hensen(Delft Tech. U.), H. Bernien(Delft Tech. U.), A.E. Dreau(Delft Tech. U.), A. Reiserer(Delft Tech. U.), N. Kalb(Delft Tech. U.) et al., Nature 526 (2015) 682-686.