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本文研究了基于4维对称信息完备正算子值测量（Symmetric Informationally Complete Positive OperatorValued Measures, SIC-POVM）和相互无偏基（Mutually Unbiased Bases, MUBs）测量的双光子量子态层析。在层析过程中，我们引入了光子计数实验中常见的干扰因素，包括泊松噪声和暗计数，以模拟真实实验环境。层析的效率通过保真度，线性熵和并发度来量化。我们发现在双光子纠缠纯态的量子态层析中，SICPOVM在抵御泊松噪声方面比MUBs具有更强的鲁棒性。这一发现挑战了以往在抵御噪声干扰时优先选择MUBs的传统观点。而对于Werner态，过完备的MUBs则能更有效地抵御泊松噪声，保障实验数据的准确性和可靠性。我们的实验结果揭示了不同测量方式在应对不同量子态时的差异性表现，为量子态层析实验中测量方案的选择提供了重要参考。
Abstract：Objective This paper aims to investigate and compare the performance of two commonly used quantum state tomography measurement schemes, namely four-dimensional SIC-POVM and MUBs, in noisy environments, in order to explore the optimal measurement strategies for different quantum states.Methods We constructed two quantum state tomography frameworks, employing 4-dimensional SIC-POVM and MUBs as the measurement schemes, respectively. During the tomography process, we introduced common interference factors in photon counting experiments, including Poisson noise and dark counts, to simulate real experimental conditions. To quantify the accuracy of the tomography, we used fidelity, linear entropy, and concurrence as evaluation indicators. Through experimental studies on two-photon entangled pure states and Werner states, we compared the performance of the two measurement schemes under noisy conditions.Results and Discussions The experimental results show that in the tomography of two-photon entangled pure states, SIC-POVM exhibits greater robustness against Poisson noise and dark counts compared to MUBs. This finding challenges the traditional view of prioritizing MUBs in noisy environments. However, for Werner states, the overcomplete MUBs exhibits superior noise resistance. This indicates that the characteristics of different quantum states have a significant impact on the choice of measurement schemes. This result further emphasizes that the selection of measurement schemes in quantum state tomography should be optimized based on the characteristics of the quantum states,rather than being applied universally.Conclusions This study reveals the significant differences in the performance of different measurement schemes when dealing with different quantum states. It highlights the importance of selecting appropriate measurement strategies in the field of quantum information processing. The choice should be tailored to both experimental objectives and the characteristics of the quantum states.
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基本信息:
中图分类号:O431.2
引用信息:
[1]杜蘅,计佳,魏毅强.基于SIC-POVM和MUBs的双光子量子态层析[J].量子光学学报,2025,31(03):20-28.
基金信息:
国家自然科学基金(12271394)