相关量子参考系过程中的最优时间隐藏
Optimal Temporal Hiding in Correlated Quantum Reference-Frame Processes
- Independent Researcher（独立研究者）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究相关量子参考系过程中的时间隐藏，将其转化为q元编码问题，给出最优隐藏条件与界限，并区分经典与相干时间隐私。
AI中文摘要：
有限群值的时间参考系定义了一个相关的随机酉过程，而不是独立信道的列表。我们确定了一个机制，在该机制中，其完整轨迹定律是一个精确的操作坐标。如果载体包含有限群 $G$ 的每个不可约表示，则一个辅助辅助输入解析所有群元素，并且对于 $G^n$ 上的任意定律 $\mu,\nu$，策略半距离等于 $d_{\mathrm{TV}}(\mu,\nu)$。最优输出侧因果后处理同样简化为 $G^n$ 上的经典卷积。这将时间隐藏转化为 $q$ 元编码问题。$[n,k]_q$ 码的均匀陪集定律在少于 $d(C^\perp)$ 个槽的每个集合上相同，并且在全局上可完美区分。对于具有从 $t$ 个选定槽泄漏至多 $\eta$ 和全局解码误差 $\epsilon$ 的 $M$ 个扇区，我们得到 $(1-\epsilon)\log M \leq (n-t)\log q+\eta+h_2(\epsilon)$。对于嵌套码 $C\subset D$，有效载荷 $R=\dim D-\dim C$，不可见深度 $t=d_{\mathrm{rel}}(C^\perp,D^\perp)-1$，以及扇区距离 $d_{\mathrm{rel}}(D,C)$ 满足 $R+t+d_{\mathrm{rel}}(D,C)-1\leq n$ 和 $R+t+2e+f\leq n$，其中 $e$ 和 $f$ 是对抗性错误和已知擦除。嵌套广义里德-所罗门码在其存在范围内达到界限。我们还给出了精确的投影秩泄漏分布，并表明从 $t$ 个槽隐藏任意相干叠加恰好是量子擦除校正，产生 $\log_q K+2t\leq n$。结果将经典轨迹隐私与相干时间隐私分开，并量化了从减少的过程断层扫描中隐藏的鲁棒有效载荷。
英文摘要：
A finite group-valued temporal reference frame defines a correlated random-unitary process rather than a list of independent channels. We identify a regime in which its complete trajectory law is an exact operational coordinate. If the carrier contains every irreducible representation of the finite group $G$, one ancilla-assisted input resolves all group elements, and for arbitrary laws $μ,ν$ on $G^n$ the strategy half-distance equals $d_{\mathrm{TV}}(μ,ν)$. Optimal output-side causal post-processing likewise reduces to classical convolution on $G^n$. This converts temporal hiding into a $q$-ary coding problem. Uniform coset laws of an $[n,k]_q$ code are identical on every set of fewer than $d(C^\perp)$ slots and perfectly distinguishable globally. For $M$ sectors with leakage at most $η$ from $t$ selected slots and global decoding error $ε$, we obtain $(1-ε)\log M \leq (n-t)\log q+η+h_2(ε)$. For nested codes $C\subset D$, the payload $R=\dim D-\dim C$, invisible depth $t=d_{\mathrm{rel}}(C^\perp,D^\perp)-1$, and sector distance $d_{\mathrm{rel}}(D,C)$ obey $R+t+d_{\mathrm{rel}}(D,C)-1\leq n$ and $R+t+2e+f\leq n$, where $e$ and $f$ are adversarial errors and known erasures. Nested generalized Reed-Solomon codes attain the bounds in their existence range. We also give the exact projection-rank leakage profile and show that hiding arbitrary coherent superpositions from $t$ slots is precisely quantum erasure correction, yielding $\log_q K+2t\leq n$. The results separate classical trajectory privacy from coherent temporal privacy and quantify the robust payload hidden from reduced process tomography.
