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arXiv:1907.07536 · Physical Review Letters

Experimental Self-Characterization of Quantum Measurements

Aonan Zhang, Jie Xie, Huichao Xu, Kaimin Zheng, Han Zhang, Yiu‐Tung Poon, Vlatko Vedral, Lijian Zhang

Published Jan 28, 2020• 26 citations
arXivHTMLPDF

Abstract

The accurate and reliable description of measurement devices is a central problem in both observing uniquely nonclassical behaviors and realizing quantum technologies from powerful computing to precision metrology. To date quantum tomography is the prevalent tool to characterize quantum detectors. However, such a characterization relies on accurately characterized probe states, rendering reliability of the characterization lost in circular argument. Here we report a self-characterization method of quantum measurements based on reconstructing the response range-the entirety of attainable measurement outcomes, eliminating the reliance on known states. We characterize two representative measurements implemented with photonic setups and obtain fidelities above 99.99% with the conventional tomographic reconstructions. This initiates range-based techniques in characterizing quantum systems and foreshadows novel device-independent protocols of quantum information applications.

DOI
10.1103/physrevlett.124.040402

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As one of the fundamental tools in the quantum information field, quantum state tomography can be utilized to reconstruct any unknown state. Usually, it needs a tomographically complete set of measurements and meantime it requires that all measurements are fully characterized. Here we propose a semi-measurement-device-independent quantum state tomography protocol, which only needs one characterized measurement and a trusted ancillary system. Furthermore, we carry out corresponding experimental demonstrations by using linear optics, and obtain the average state fidelity as high as 0.973, verifying the effectiveness of the scheme.
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Improving accuracy of quantum operations is an indispensable task for realizing a practical quantum computer. A reliable method for characterizing quantum operations is a useful tool towards further improvements of the accuracy. Quantum tomography and randomized benchmarking protocols are current standard methods for evaluating accuracies of quantum operations, but their estimates lack reliability because of high sensitivity to state preparation and measurement (SPAM) errors or they use multiple approximations. Here we propose a self-consistent quantum tomographic method. First, we derive a sufficient condition on experiments for characterizing quantum operations except for the gauge degrees of freedom. Second, we propose a new self-consistent estimator. We mathematically prove that, when the sufficient condition is satisfied, the estimator provides estimates that are always physical and converge to the gauge-equivalence class of the quantum operations of interest at the limit of data size going to infinity. We also derive the rate of the asymptotic convergence. These results theoretically guarantee that the method makes it possible to reliably characterize accurate quantum operations.