Pre-Channel Entanglement Shaping Achieves Fundamental Superiority over Post-Distillation: A Geometric Entropy Perspective
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914571202068480 |
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| author | Lyu, Gang Sun, Wenlong Jin, Yuanfeng Nan, Hua |
| author_facet | Lyu, Gang Sun, Wenlong Jin, Yuanfeng Nan, Hua |
| contents | Traditional entanglement distillation follows a post-processing paradigm, a noisy quantum state, after full transmission through a noisy channel, is treated as a static resource to be purified via LOCC (local operations and classical communication). This work demonstrates a fundamentally different paradigm,pre-channel entanglement shaping (PES) -- actively engineering the system-environment coupling before or during channel transmission -- achieves a level of purification capability that is physically unattainable by any post-distillation protocol. We prove this separation using the framework of geometric entropy (quantum relative entropy to separable states). In post-distillation, the protocol can only select low-entropy sub-ensembles from a fixed mixed state, leaving the global geometric entropy unchanged or increased. In contrast, PES \textit{suppresses the rate of geometric entropy production} during channel evolution, resulting in a final state whose relative entropy of entanglement strictly exceeds the maximum achievable by post-distillation from the same channel. We provide explicit qubit channel examples, numerical simulations (with complete code in Appendix), and a geometric interpretation on the state manifold. Our result establishes pre-channel entanglement shaping as a distinct operational resource class, with immediate implications for quantum repeaters and entanglement-assisted communication. Very recently, Li \textit{et al.} experimentally demonstrated that preprocessing the entangling channel with optimally tailored local unitaries achieves entanglement fidelities unreachable by any postprocessing, revealing an intrinsic temporal asymmetry in entanglement distillation~\cite{Li2025}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_16463 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pre-Channel Entanglement Shaping Achieves Fundamental Superiority over Post-Distillation: A Geometric Entropy Perspective Lyu, Gang Sun, Wenlong Jin, Yuanfeng Nan, Hua Quantum Physics Operator Algebras Primary: 81P45, 81P40, Secondary: 94A40, 81P15, 53Z05, 82C10 B.4.5; F.1.1; E.4; F.2.2 Traditional entanglement distillation follows a post-processing paradigm, a noisy quantum state, after full transmission through a noisy channel, is treated as a static resource to be purified via LOCC (local operations and classical communication). This work demonstrates a fundamentally different paradigm,pre-channel entanglement shaping (PES) -- actively engineering the system-environment coupling before or during channel transmission -- achieves a level of purification capability that is physically unattainable by any post-distillation protocol. We prove this separation using the framework of geometric entropy (quantum relative entropy to separable states). In post-distillation, the protocol can only select low-entropy sub-ensembles from a fixed mixed state, leaving the global geometric entropy unchanged or increased. In contrast, PES \textit{suppresses the rate of geometric entropy production} during channel evolution, resulting in a final state whose relative entropy of entanglement strictly exceeds the maximum achievable by post-distillation from the same channel. We provide explicit qubit channel examples, numerical simulations (with complete code in Appendix), and a geometric interpretation on the state manifold. Our result establishes pre-channel entanglement shaping as a distinct operational resource class, with immediate implications for quantum repeaters and entanglement-assisted communication. Very recently, Li \textit{et al.} experimentally demonstrated that preprocessing the entangling channel with optimally tailored local unitaries achieves entanglement fidelities unreachable by any postprocessing, revealing an intrinsic temporal asymmetry in entanglement distillation~\cite{Li2025}. |
| title | Pre-Channel Entanglement Shaping Achieves Fundamental Superiority over Post-Distillation: A Geometric Entropy Perspective |
| topic | Quantum Physics Operator Algebras Primary: 81P45, 81P40, Secondary: 94A40, 81P15, 53Z05, 82C10 B.4.5; F.1.1; E.4; F.2.2 |
| url | https://arxiv.org/abs/2605.16463 |