AI 中文总结
本研究针对量子数据隐藏问题，在 bipartite 系统等场景下，推导了不同受限测量下的最优数据隐藏比，强化了经典可分球定理并改进了相关上界。
AI 中文摘要
量子数据隐藏研究的是，当全局测量被限制为局域测量与经典通信时，可区分能力会损失多少。在本研究中，我们针对几类自然的受限测量建立了精确结果与改进界。对于ℂⁿ⊗ℂᵐ上的 bipartite 系统，我们证明，针对可分测量与 LOCC 测量的最优数据隐藏比均为min{n,m}。该结果源于一个更强的结论：对每个2≤p≤∞，其关联二值测量可通过有限轮 LOCC 实现的最大中心 Schatten p-球的半径为min{n,m}^{2/p-1}。这一结论强化了经典可分球定理，同时提供了明确的有限轮 LOCC 实现方案。对于 Alice 优先的单向 LOCC，当 Alice 的局域维度为n时，我们证明最优比为(1+o(1))n，其上界由高斯秩一 POVM 得到。对于无通信的局域操作，我们将通用上界改进为(π√3/4+o(1))min{n,m}。
英文摘要
Quantum data hiding asks how much distinguishing power can be lost when global measurements are restricted to local measurements and classical communication. In this work, we establish sharp results and improved bounds for several natural classes of restricted measurements. For bipartite systems on $\mathbb C^n\otimes\mathbb C^m$, we prove that the optimal data-hiding ratios against separable and LOCC measurements are both $\min\{n,m\}$. This result follows from a stronger result that, for every $2\le p\le\infty$, the largest centered Schatten $p$-ball whose associated binary measurements are implementable by finite-round LOCC has radius $\min\{n,m\}^{2/p-1}$. This strengthens the classic separable-ball theorems, while also providing an explicit finite-round LOCC implementation. For Alice-first one-way LOCC with Alice's local dimension equal to $n$, we prove that the optimal ratio is $(1+o(1))n$, with the upper bound obtained from a Gaussian rank-one POVM. For local operations without communication, we improve the universal upper bound to $(π\sqrt3/4+o(1))\min\{n,m\}$.
