超越有限维度的量子信息解耦
Quantum Information Decoupling Beyond Finite Dimensions
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中文总结 AI 辅助
本文建立了适用于任意可分系统的量子信息解耦框架，推导了相关误差界，构造了无限维度解耦协议及量子态合并协议，证明了熵量操作解释的普适性。
中文摘要 AI 辅助
量子信息解耦是量子信息理论的核心支柱，是量子通信、量子纠错和信息恢复的基础。然而，其现有表述依赖与量子系统有限维度假设绑定的随机幺正操作。本文建立了适用于任意可分、可能为无限维度系统的解耦框架。针对有限维度输入和任意可分参考/输出系统，我们用夹层Rényi条件熵推导了完全正映射的单份解耦误差界；针对参考为有限维度的部分迹解耦，误差指数在已知临界速率下达到最优。为处理无限维度输入，我们假设被操作系统具有有限熵，在独立同分布（IID）态上构造有限秩投影，将随机化限制在投影后的有限维度子空间，同时通过在被丢弃子系统中加入辅助分量，以渐近可忽略的成本确保高成功概率。这一方法实现了无限维度IID部分迹解耦协议，达到最优渐近维度速率。作为应用，我们构造了无限维度量子态合并协议（量子信息理论的母协议），在Alice的边际具有有限熵的条件下，其量子通信和总代价速率与有限维度情形相同，由互信息和条件熵决定。这些结果表明，通过这些可达速率对熵量的操作解释构成了超越有限维度的普适原理，更广泛而言，我们的框架为探索量子信息提供了基础工具，无论我们用有限还是无限维度空间建模物理世界。
英文摘要
Quantum information decoupling is a pillar of quantum information theory, underlying quantum communication, error correction, and information recovery. However, its existing formulations rely on random unitary operations tied to finite-dimensional assumptions on quantum systems. Here we establish a decoupling framework for arbitrary separable, possibly infinite-dimensional systems. For finite-dimensional inputs and arbitrary separable reference/output systems, we derive error bounds on one-shot decoupling for completely positive maps in terms of sandwiched Rényi conditional entropies. For partial-trace decoupling with finite-dimensional references, the error exponent is optimal up to the known critical rate. To handle infinite-dimensional inputs, we assume finite entropy of the manipulated system. We construct finite-rank projections on independent and identically distributed (IID) states to restrict randomization to a projected finite-dimensional subspace, while ensuring high success probability by including auxiliary components in the discarded subsystem at asymptotically negligible cost. This leads to an infinite-dimensional IID partial-trace decoupling protocol achieving optimal asymptotic dimension rates. As an application, we construct an infinite-dimensional quantum-state-merging protocol, a mother protocol of quantum information theory. Under finite entropy of Alice's marginal, it achieves the same quantum-communication and total-cost rates as in finite dimensions, governed by mutual information and conditional entropy. These results show that the operational interpretation of entropic quantities through these achievable rates constitutes a universal principle beyond finite dimensions. More broadly, our framework provides foundational tools for exploring quantum information regardless of whether we model the physical world using finite- or infinite-dimensional spaces.
