Quantum shape shifting. Molecular nanostructures of different shape (top and bottom surfaces), linked topologically (beam) to share the same spectrum, enable the measurement of quantum mechanical phase. Background: color-encoded quantum state transplantation matrix.

A wrinkle in space. Two quantum nanostructures of different shape (top and bottom surfaces) can be linked topologically to “sound the same,” enabling the measurement of quantum mechanical phase (background).

Nanoassembly of “quantum drums” enables measurement of quantum mechanical phase. Background: color-encoded quantum state transplantation matrix.

Geometry over interferometry. Geometric tuning of quantum materials enables the measurement of normally forbidden quantum mechanical phase information.

Quantum isospectrality. Sounds generated from the average spectra acquired inside the Bilby, Hawk, and Broken Hawk shapes. Each sound is repeated 8 times as the topograph of the corresponding quantum drum is highlighted. Bilby and Hawk—which are isospectral—“sound the same,” while Broken Hawk can be audibly distinguished.

Quantum homophonicity. Audio conversion of 3 pairs of point spectra acquired within the isospectral Aye-aye and Beluga shapes. The similarity between the homophonic points is audibly contrasted with the easily discernable differences between other points. Each sound is repeated 4 times as the topograph of the corresponding nanostructure is highlighted and the position of the acquired spectrum is identified with a red cross.

Quantum transplantation. Full phase extraction process for modes 1 to 3 of the Aye-aye (A) and Beluga (B) quantum resonators. The algorithm is represented by a black box, the quantum transplantation machine (QTM), which has the goal of obtaining the full wave functions including all amplitude and phase information. Chapter headings, matching audio narration, can be selected to jump to specific QTM states.