Sahoo Surya Narayan, Chakraborti Sanchari, Pati Arun K, Sinha Urbasi
Light and Matter Physics, Raman Research Institute, Bengaluru 560080, India.
Quantum Information and Computation Group, Harish-Chandra Research Institute, HBNI, Allahabad 211019, India.
Phys Rev Lett. 2020 Sep 18;125(12):123601. doi: 10.1103/PhysRevLett.125.123601.
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}.
量子态层析成像（QST）一直是表征未知量子态的传统方法。最近，已经实现了许多直接测量方法，以资源高效的方式重构量子态。在本信函中，我们提出了一种干涉测量方法，其中，使用单次测量，从干涉图样的可见度、相移和平均强度可以推断出任何量子比特态，无论是混合态还是纯态——因此，我们将其称为量子态干涉成像。这为我们提供了一种量子态估计的“黑箱”方法，即在光子入射和提取态信息之间，我们不改变装置内的任何条件，从而实现对量子态的真正单次估计。相比之下，标准的QST对于纯态量子比特至少需要两次测量，对于混合态量子比特重构至少需要三次测量。然后，我们继续表明，对于纯二分量子比特中的纠缠量化，量子态干涉成像（QSI）比量子态层析成像（QST）更具资源效率。我们利用光的偏振自由度，以高保真度通过实验实现了我们的方法。还提出了该方案对涉及d维系统的d - 1个干涉图样的纯态的扩展。因此，对于我们的方法，在量子d比特情形下，缩放增益更为显著，相比之下，标准的QST在没有任何假设的情况下，缩放比例大致为d² 。
