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.
A quantum eraser is proposed that operates in a domain that does not have any classical counterpart. This quantum eraser utilizes the complementary aspect between entanglement and single-partite properties of composite quantum systems. Consequently, in contrast to the duality of visibility and which-path information which establish features of single quantum systems, here, properties of composite quantum systems are considered. In composite quantum systems entanglement might emerge which is of genuine quantum origin. This nonclassical correlation mutually exclude the single-partite properties of the subsystems of the composite quantum system. The single-partite properties can be describes by wave- and particle properties, i.e. the standard wave-particle duality. Remarkably, entanglement can be considered as a resource for observables that do not exist in classical physics. In a bipartite photon system, this observable is the two-particle visibility which describes the phase relations that are shared between both photons of the composite system. The complementary aspect between two-particle visibility and single-partite properties of the subsystems prevents us from the observation of single-partite properties in an entangled biphoton system. The quantum eraser erases the two-partite visibility and retrieves single-partite properties in form of single-particle visibility for both of the two photons. Thus, both observables contain phase information giving rise to interference effects. Here, complementarity is explicitly enforced by entanglement in a quantitative manner.