Bloch tensors for arbitrary-party pure symmetric qubit states

Express the general tensors appearing in the Bloch representation of pure permutation-symmetric qubit states with an arbitrary number of parties in terms of the states’ Majorana constellations.

Background

The paper derives explicit relations between Majorana constellations and generalized Bloch-representation parameters for pure qudit states and for pure permutation-symmetric two- and three-qubit states. For two qubits, the Bloch vector and correlation matrix are expressed using the two Majorana stars; for three qubits, the corresponding first-, second-, and third-order correlation tensors are expressed using the three stars.

The stated unresolved extension is to arbitrary numbers of parties: determine formulas relating every tensor in the Bloch representation of a pure symmetric multiqubit state to its Majorana constellation. Such formulas would extend the paper’s two- and three-qubit results to the general permutation-symmetric qubit setting.

References

An important open question is how to express, for pure symmetric qubit states of arbitrary number of parties, the general tensors appearing in the Bloch representation in terms of the Majorana constellation.

— From Majorana to Bloch: two ways to generalize the Bloch sphere representation  (2610.11868 - Hanotel, 8 Oct 2026) in Section 6, Conclusions

Furthermore, it would be interesting to explore whether those relations can be extended even beyond symmetric states or even pure states, taking, for example, the generalization of the Majorana representation for arbitrary states found in .

— From Majorana to Bloch: two ways to generalize the Bloch sphere representation  (2610.11868 - Hanotel, 8 Oct 2026) in Section 6, Conclusions