发表机构
Harvard University; University of Washington; Stanford University（哈佛大学; 华盛顿大学; 斯坦福大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
我们提出高效协议，对任意玻色子态进行无假设层析成像，输出保真度损失接近最优的纯高斯态，并证明非高斯测量对强保证的必要性及经典鲁棒估计的局限性。
AI 中文摘要
我们研究了纯玻色子高斯态的无假设层析成像：给定任意$n$模玻色子态$\rho$的副本，目标是输出一个纯高斯态，其与$\rho$的保真度损失至多为$\mathrm{opt} + \epsilon$，其中$\mathrm{opt}$是任何纯高斯态可达到的最小保真度损失。我们在高保真度和低保真度两种情况下都给出了高效协议。当$\mathrm{opt}$低于某个通用常数时，我们的协议的运行时间和副本复杂度在$n, 1/\epsilon$和$\log \log E$上是强多项式的，其中$E$是最接近的纯高斯态的能量。对于任意的$\mathrm{opt}$，我们的协议使用$(n+1)^{\mathrm{poly}(1/\epsilon)} \mathrm{poly}\left(1+\log\log(E)\right)$个副本和相应运行时间。作为推论，我们获得了第一个真正容忍的高斯性测试协议，用于区分$\mathrm{opt} > c + \epsilon$或$\mathrm{opt} < c - \epsilon$，适用于任何阈值$c\in(0,1)$。我们还证明了$\mathrm{poly}(n,1/\epsilon)$运行时间是不可能的，除非$\mathrm{NP}\subseteq\mathrm{BQP}$。我们的协议遵循一个共同范式：首先，我们迭代地使用一般高斯测量结合经典鲁棒统计技术来获得良好的热启动估计，然后我们利用非高斯测量通过凸和非凸优化方法细化这个热启动。有趣的是，我们证明了非高斯测量对于匹配我们获得的强无假设保证是必要的，事实上，这些保证被证明优于对经典高斯分布进行鲁棒估计所能达到的效果。
英文摘要
We study agnostic tomography of pure bosonic Gaussian states: given copies of an arbitrary $n$-mode bosonic state $ρ$, the goal is to output a pure Gaussian state whose infidelity with $ρ$ is at most $\mathrm{opt} + ε$, where $\mathrm{opt}$ is the minimum infidelity achievable by any pure Gaussian state. We give efficient protocols achieving this in both the high and low fidelity regimes. When $\mathrm{opt}$ is below some universal constant, our protocol has runtime and copy complexity which is strongly polynomial in $n, 1/ε$ and $\log \log E$, where $E$ is the energy of the closest pure Gaussian state. For arbitrary $\mathrm{opt}$, our protocol uses $(n+1)^{\mathrm{poly}(1/ε)} \mathrm{poly}\left(1+\log\log(E)\right)$ copies and runtime. As a corollary, we obtain the first truly tolerant Gaussianity testing protocol for distinguishing whether $\mathrm{opt} > c + ε$ or $\mathrm{opt} < c - ε$, for any threshold $c\in(0,1)$. We also prove $\mathrm{poly}(n,1/ε)$ runtime is impossible, unless $\mathrm{NP}\subseteq\mathrm{BQP}$. Our protocols follow a shared paradigm: first, we iteratively use general Gaussian measurements combined with techniques from classical robust statistics to obtain a good warm start estimate, then we leverage non-Gaussian measurements to refine this warm start using convex and non-convex optimization methods. Interestingly, we prove that non-Gaussian measurements are necessary to match the strong agnostic guarantees we obtain, and in fact these guarantees are provably superior to what is possible for robustly estimating classical Gaussians.
Comments83 pages
