Geometric quantifier of the incompatibility of single-particle property attribution in indistinguishable boson systems

Abstract:Entanglement in indistinguishable particle systems can be characterized by the impossibility of unambiguously attributing a complete set of physical properties to the individual constituent particles. In this work, we introduce a geometric quantifier of the incompatibility of such simultaneous property attribution for pure states of $N$ indistinguishable bosons. Using the Majorana stellar representation, any symmetric multi-qubit state can be expressed as the symmetrization of constituent single-particle states, allowing the associated single-particle properties to be directly linked with the corresponding Majorana stars. This establishes a direct connection between the geometry of the Majorana representation on the Bloch sphere and the entanglement criterion based on the attribution of single-particle properties in systems of identical two-level bosons. We then generalize this geometric approach to higher-dimensional bosons, extending the quantifier from qubits to qudits, while retaining a geometric interpretation of property-attribution incompatibility in terms of Fubini-Study angles.

arXiv:2609.17256 [quant-ph]

(or arXiv:2609.17256v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.17256 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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