Recently introduced shadow tomography protocols use classical shadows of quantum states to predict many target functions of an unknown quantum state. Unlike full quantum state tomography, shadow tomography does not insist on accurate recovery of the density matrix for high rank mixed states. Yet, such a protocol makes multiple accurate predictions with high confidence, based on a moderate number of quantum measurements. One particular influential algorithm, proposed by Huang, Kueng, and Preskill arXiv:2002.08953, requires additional circuits for performing certain random unitary transformations. In this paper, we avoid these transformations but employ an arbitrary informationally complete POVM and show that such a procedure can compute k-bit correlation functions for quantum states reliably. We also show that, for this application, we do not need the median of means procedure of Huang et al. Finally, we discuss the contrast between the computation of correlation functions and fidelity of reconstruction of low rank density matrices.
翻译:最近引入的影子透视协议使用量子状态的经典阴影来预测未知量子状态的许多目标函数。 与完整的量子状态断层不同, 影子透视并不坚持要准确恢复高等级混杂状态的密度矩阵。 然而, 这样的协议根据数量测量的适度数量, 以高度信心做出多次准确预测。 由黄、 Kueng 和 Preskill arXiv: 2002. 08. 953 提出的一个特别有影响力的算法需要额外的电路来进行某些随机单一变换。 在本文中, 我们避免了这些变换, 但却使用了一个任意的信息完整的 POVM, 并表明这样的程序可以可靠地计算量子状态的 k- 比特相关函数 。 我们还表明, 对于这一应用, 我们不需要黄等人的中位手段程序。 最后, 我们讨论相关函数的计算和低级密度矩阵重建的准确性之间的对比。