Quantum information cannot be broadcast—an intrinsic limitation imposed by quantum mechanics. However, recent advances in virtual operations offer new insights into the no-broadcasting theorem. Here, we focus on the practical utility and introduce sample efficiency as a fundamental constraint, requiring any practical broadcasting protocol perform no worse than the naive approach of direct preparation and distribution. We prove that no linear process—whether quantum or beyond—can simultaneously uphold sample efficiency, unitary covariance, permutation invariance, and classical consistency. This leads to a no-practical-broadcasting theorem, which places strict limits on the practical distribution of quantum information. By applying Schur-Weyl duality, we establish the uniqueness of the canonical 1-to-$N$ virtual broadcasting map that satisfies the latter three conditions, provide its construction, and determine its sample complexity through semidefinite programming. Finally, we explore the interplay between virtual broadcasting and a quantum spacetime framework, known as the pseudodensity operator, showing that their correspondence holds only in the 1-to-2 case, underscoring the fundamental asymmetry between spatial and temporal statistics in the quantum world.

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• Quantum correlations, foundations & formalism
• Quantum foundations
• Quantum information theory