Precision Bounds on Continuous-Variable State Tomography Using Classical Shadows
Precision Bounds on Continuous-Variable State Tomography Using Classical Shadows
复制标题
使用经典阴影的连续可变状态断层扫描的精度范围
作者：
Srilekha Gandhari;Victor V. Albert;T. Gerrits;Jacob M. Taylor;M. Gullans
阴影层析成像是一个框架，用于使用随机测量基（称为经典阴影）构建量子态的简洁描述，并具有强大的方法来约束所使用的估计量。我们重铸现有的连续变量量子态层析成像的经典阴影框架的实验协议，获得严格的界限估计密度矩阵从这些协议所需的独立测量的数量。我们分析了零差，外差，光子数分辨（PNR）和光子奇偶校验协议的效率。为了达到期望的精度上的经典阴影的$N$-光子密度矩阵具有很高的概率，我们表明，零差检测需要一个命令$mathcal{O}（N^{4+1/3}）$测量在最坏的情况下，而PNR和光子奇偶检测需要$mathcal{O}（N ^{4+1/3}）$测量在最坏的情况下（都达到对数校正）。我们基准这些结果对数值模拟以及光学零差实验的实验数据。我们发现，数值和实验的零差层析显着优于我们的界限，表现出更典型的缩放的测量的数量是接近线性的$N$。我们扩展我们的单模式的结果，一个有效的建设多模阴影的基础上，当地的测量。
Shadow tomography is a framework for constructing succinct descriptions of quantum states using randomized measurement bases, called classical shadows, with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable quantum state tomography in the classical-shadow framework, obtaining rigorous bounds on the number of independent measurements needed for estimating density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon number resolving (PNR), and photon-parity protocols. To reach a desired precision on the classical shadow of an $N$-photon density matrix with a high probability, we show that homodyne detection requires an order $mathcal{O}(N^{4+1/3})$ measurements in the worst case, whereas PNR and photon-parity detection require $mathcal{O}(N^4)$ measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental homodyne tomography significantly outperforms our bounds, exhibiting a more typical scaling of the number of measurements that is close to linear in $N$. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements.
影响因子：
56.9
作者：
Huang, Hsin-Yuan;Kueng, Richard;Preskill, John
通讯作者：
Preskill, John