量子记忆在量子过程重构中的优势
Quantum memory advantage for quantum process tomography
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中文总结 AI 辅助
本研究证明了量子记忆在量子过程重构中提供查询复杂性优势，通过确定无量子记忆协议的最优复杂度并展示非相干协议的上界。
中文摘要 AI 辅助
量子过程重构，即通过黑盒访问学习未知量子通道的任务，是量子信息中的核心问题。在这一设定中，具有量子记忆的协议可以相干地存储并联合处理从多个通道使用中获得的量子信息，而没有量子记忆的协议必须在每次使用后测量，并仅保留测量结果的古典记录。一个根本性的开放问题是，即使在没有量子记忆的协议可能基于所有先前结果利用无界经典计算能力的情况下，量子记忆是否提供查询复杂性优势。在本工作中，我们证明了确实如此。我们确定了在没有量子记忆的情况下量子过程重构的最优查询复杂性，直到常数因子，为Θ(d_in^3 d_out^3/ε^2)，其中d_in和d_out分别是通道输入和输出维度，ε是目标钻石范数精度。更准确地说，我们证明了任何非相干协议（包括自适应协议）对于此任务都需要Ω(d_in^3 d_out^3/ε^2)次查询，即使每次通道使用可能由任意新鲜辅助系统辅助，并且我们提出了一个非自适应、无辅助系统的非相干协议，实现了匹配的上界O(d_in^3 d_out^3/ε^2)。我们的结果因此扩展了单份态重构的最优样本复杂度界限，作为特殊情况d_in=1恢复。相比之下，具有量子记忆的相干协议实现查询复杂度Θ(d_in^2 d_out^2/ε^2)。因此，我们的结果建立了量子过程重构有无量子记忆之间的严格学习分离。
英文摘要
Quantum process tomography, the task of learning an unknown quantum channel from black-box access, is a central problem in quantum information. In this setting, protocols with quantum memory can coherently store and jointly process quantum information obtained from multiple channel uses, whereas protocols without quantum memory must measure after each use and retain only a classical transcript of the measurement outcomes. A fundamental open question is whether quantum memory provides a query-complexity advantage even when protocols without quantum memory may adapt their experiments based on all previous outcomes with unbounded classical computational power. In this work, we show that it does. We determine the optimal query complexity of quantum process tomography without quantum memory up to a constant factor to be $Θ(d_{\mathrm{in}}^3 d_{\mathrm{out}}^3/\varepsilon^2)$, where $d_{\mathrm{in}}$ and $d_{\mathrm{out}}$ are the channel input and output dimensions, respectively, and $\varepsilon$ is the target diamond-norm accuracy. More precisely, we prove that any incoherent protocol for this task, including adaptive protocols, requires $Ω(d_{\mathrm{in}}^3 d_{\mathrm{out}}^3/\varepsilon^2)$ queries, even when each channel use may be assisted by arbitrary fresh ancilla, and we present a non-adaptive, ancilla-free incoherent protocol achieving the matching upper bound $O(d_{\mathrm{in}}^3 d_{\mathrm{out}}^3/\varepsilon^2)$. Our results thereby generalize the optimal sample-complexity bounds for single-copy state tomography, recovered as the special case $d_{\mathrm{in}}=1$. By contrast, coherent protocols with quantum memory achieve query complexity $Θ(d_{\mathrm{in}}^2 d_{\mathrm{out}}^2/\varepsilon^2)$. Hence, our results establish a rigorous learning separation between quantum process tomography with and without quantum memory.
