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.
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BibTeX
@misc{cespedes2026geometric,
title = {{Geometric quantifier of the incompatibility of single-particle property attribution in indistinguishable boson systems}},
author = {P. Céspedes and A. Valdés-Hernández and F. H. Holik and A. P. Majtey},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17256},
eprint = {2609.17256},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17256},
}
RIS
TY - UNPB
TI - Geometric quantifier of the incompatibility of single-particle property attribution in indistinguishable boson systems
AU - P. Céspedes
AU - A. Valdés-Hernández
AU - F. H. Holik
AU - A. P. Majtey
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17256
UR - https://arxiv.org/abs/2609.17256
AB - 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.
ER -