超越纯态的量子纠缠蒸馏计算：高效协议与基本限制
Computational entanglement distillation beyond pure states: efficient protocols and fundamental limitations
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中文总结 AI 辅助
本研究针对混合态纠缠蒸馏，确定Rényi相干信息为最坏情况下的最优速率，并设计了无需输入态知识的通用样本高效协议及高效协议，赋予其新的操作意义。
中文摘要 AI 辅助
量子纠缠的信息论方法通常依赖于任意多的输入副本和无限复杂的操作；然而，实际中可用资源是受限的。这促使了在有限资源下研究纠缠理论。其核心问题之一是哪些量能够刻画纠缠操作，而迄今为止，只有纯态的理想化情况得到了充分探索。在本工作中，我们研究了混合态的纠缠蒸馏，并确定Rényi相干信息是在两种不同资源约束下最坏情况下决定最优速率的量。我们首先刻画了样本高效区域，其中允许无限计算能力。我们的通用协议在一定的多项式秩约束下，无需输入态知识即可达到该速率。该速率在通用协议中是最优的：我们构造了其可蒸馏纠缠近乎广延的状态，然而没有任何通用样本高效协议能够达到高于其Rényi相干信息的速率。然后，我们将这一刻画推进到计算高效前沿：即使输入态已知，任何高效协议也满足相同的界限，并且另一个通用协议在边际秩的额外多项式约束下能够高效地达到该速率。总体而言，我们的结果赋予Rényi相干信息在两个计算设置中新的操作意义：有限副本下的通用蒸馏以及即使已知输入态的高效蒸馏。
英文摘要
The information-theoretic approach to entanglement typically relies on arbitrarily many input copies and unboundedly complex operations; however, the available resources are constrained in reality. This motivates the study of entanglement theory with limited resources. One of its central questions is which quantities characterize entanglement manipulations, and so far, only the idealized case of pure states has been well explored. In this work, we address entanglement distillation from mixed states and identify the Rényi coherent information as the quantity determining the optimal rate in the worst case under two distinct resource constraints. We first characterize the sample-efficient regime, in which unbounded computational power is allowed. Our universal protocol achieves this rate without knowledge of the input state under certain polynomial rank constraints. This rate is optimal among universal protocols: we construct states whose distillable entanglement is nearly extensive, yet from which no universal sample-efficient protocol attains a rate above their Rényi coherent information. We then push this characterization to the computationally efficient frontier: the same bound holds for any efficient protocol even when the input state is known, and another universal protocol achieves this rate efficiently under additional polynomial constraints on the marginal ranks. Overall, our results give the Rényi coherent information a novel operational meaning in two computational settings: universal distillation with limited copies and efficient distillation even with knowledge of the input state.
发表机构
- The University of Tokyo（东京大学）
- Freie Universität Berlin（柏林自由大学）
- Università degli Studi di Salerno（萨莱诺大学）
- Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）
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