Lewis, got it! Makes so much more sense now.

Thank you very much for your interest in this work. Unfortunately the paper link provided with the initial release was incorrect. For those interested the correct paper the title is Quantum hypercube states and the link is:

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.020402

Here is the abstract,

We introduce quantum hypercube states, a class of continuous-variable quantum states that are generated as orthographic projections of hypercubes onto the quadrature phase space of a bosonic mode. In addition to their interesting geometry, hypercube states display phase-space features much smaller than Planck’s constant, and a large volume of Wigner negativity. We theoretically show that these features make hypercube states sensitive to displacements at extremely small scales in a way that is surprisingly robust to initial thermal occupation and to small separation of the superposed state components. In a high-temperature proof-of-principle optomechanics experiment we observe, and match to theory, the signature outer-edge vertex structure of hypercube states.