No Practical Quantum Broadcasting: Even Virtually
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912614131433472 |
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| author | Xiao, Yunlong Liu, Xiangjing Liu, Zhenhuan |
| author_facet | Xiao, Yunlong Liu, Xiangjing Liu, Zhenhuan |
| contents | 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 naïve 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 pseudo-density 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16380 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | No Practical Quantum Broadcasting: Even Virtually Xiao, Yunlong Liu, Xiangjing Liu, Zhenhuan Quantum Physics 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 naïve 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 pseudo-density 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. |
| title | No Practical Quantum Broadcasting: Even Virtually |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2503.16380 |