Quantum state tomography (QST) has been the traditional method for characterization of an unknown state. Recently, many direct measurement methods have been implemented to reconstruct the state in a resource efficient way. In this Letter, we present an interferometric method, in which any qubit state, whether mixed or pure, can be inferred from the visibility, phase shift, and average intensity of an interference pattern using a single-shot measurement—hence, we call it quantum state interferography. This provides us with a “black box” approach to quantum state estimation, wherein, between the incidence of the photon and extraction of state information, we are not changing any conditions within the setup, thus giving us a true single shot estimation of the quantum state. In contrast, standard QST requires at least two measurements for pure state qubit and at least three measurements for mixed state qubit reconstruction. We then go on to show that QSI is more resource efficient than QST for quantification of entanglement in pure bipartite qubits. We experimentally implement our method with high fidelity using the polarization degree of freedom of light. An extension of the scheme to pure states involving $d-1$ interferograms for $d$-dimensional systems is also presented. Thus, the scaling gain is even more dramatic in the qudit scenario for our method, where, in contrast, standard QST, without any assumptions, scales roughly as $d^2$.

中文翻译：

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量子态干涉图

量子状态层析成像（QST）是表征未知状态的传统方法。近来，已经实现了许多直接测量方法以资源有效的方式重建状态。在这封信中，我们介绍了一种干涉测量方法，其中可以通过单次测量从干涉图的可见性，相移和平均强度推断出任何量子位状态，无论是混合状态还是纯状态，因此，我们将其称为量子态干涉图。这为我们提供了一种“黑匣子”方法来进行量子态估计，其中，在光子入射和状态信息提取之间，我们不会更改设置中的任何条件，从而为我们提供了对量子的真实单发估计州。相反，标准QST对于纯状态量子位至少需要两次测量，对于混合状态量子位至少需要至少三个测量。然后，我们继续证明，对于纯二分量子位中的纠缠量化，QSI比QST更具资源效率。我们利用光的偏振自由度实验性地实现了高保真度的方法。将该方案扩展到涉及以下方面的纯状态$d-\mathrm{1个}$ 的干涉图 $d$维系统也被提出。因此，在我们的方法的Qudit方案中，缩放增益甚至更加显着，相比之下，在没有任何假设的情况下，标准QST的缩放幅度大致为$d^2$。