Interpret the Lorentz-transformational meaning of non-Hermitian qubit evolution

Determine whether the correspondence between non-Hermitian qubit time evolution and Lorentz transformations of null vectors has a deeper meaning, including whether the evolution can be interpreted as a change of observer or as a mapping in a two-dimensional space.

Background

The paper represents a non-Hermitian qubit density operator using a null vector in spacetime algebra and identifies its time evolution with a proper orthochronous Lorentz transformation on the future light cone. After restoring the trace normalization, the transformed Bloch-like vector can be viewed in terms of a transformed observer frame. The authors explicitly state that the conceptual significance of this correspondence remains unresolved, and they further suggest possible interpretations involving observer changes and mappings on the celestial sphere.

References

Although we have shown how the time evolution of a state connects to a Lorentz transformation of a null vector, it is still unclear whether there is any deeper meaning behind it.

— Non-Hermitian Generalization of Bloch Sphere in Spacetime Algebra  (2608.23232 - Wang, 24 Aug 2026) in Section 'Discussion and Future Directions'

Another important question is whether we can generalize this picture to multi-qubit cases. A possible way is to follow by using the multi-particle spacetime algebra (MSTA). However, how to treat the pseudoscalars from different particles consistently may become a subtle problem. Again, we will leave this problem to a future exploration.

— Non-Hermitian Generalization of Bloch Sphere in Spacetime Algebra  (2608.23232 - Wang, 24 Aug 2026) in Section 'Discussion and Future Directions'