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Relying on a mathematical analogy of the pure states of the two-qubit systemof quantum information theory with four-component spinors we introduce theconcept of the intrinsic entanglement of spinors. To explore its physical sensewe study the entanglement capabilities of the spin representation of (pseudo-)conformal transformations in (3+1)-dimensional Minkowski space-time. We findthat only those tensor product structures can sensibly be introduced in spinorspace for which a given spinor is not entangled.

Entanglement capabilities of the spin representation of (3+1)D-conformal transformations