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基于量子导引的弱纠缠检测

丘尚锋 徐桥 周晓祺

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基于量子导引的弱纠缠检测

丘尚锋, 徐桥, 周晓祺

Detection of Weak Entanglement Based on Quantum Steering

QIU Shangfeng, XU Qiao, ZHOU Xiao-qi
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  • 纠缠是量子理论中一种独特的现象, 揭示了经典物理与量子物理之间的根本差异. 虽然在微观尺度上已经观察到许多纠缠现象, 但当涉及大尺度系统的相互作用时, 纠缠往往非常微弱, 此时实验设备的误差可能掩盖微弱信号, 导致纠缠难以测得. 为了提升对微弱纠缠信号的检测灵敏度, 最近提出了一种基于量子导引的弱纠缠判据, 可以有效地检测微弱的纠缠态. 我们在理论上证明了该判据相比于传统纠缠目击者判据在弱纠缠检测能力方面具有明显优势. 此外, 我们通过光学实验验证了这一判据的可行性, 实验结果为其有效性提供了关键支持, 并展示了该判据在弱纠缠态检测中的创新性和可靠性. 该判据作为一种有效的弱纠缠检测手段, 有望在量子通信、量子计算等量子技术领域中得到广泛应用.
    Quantum entanglement is a defining feature of quantum mechanics and lies at the heart of many quantum technologies. While entanglement is routinely observed in small-scale systems, detecting weak entanglement in large or noisy systems remains a significant challenge, as experimental imperfections can easily obscure fragile quantum correlations. A new weak entanglement detection criterion based on quantum steering has recently been proposed as a potential alternative to conventional entanglement witnesses. In this work, we provide a theoretical analysis comparing the detection capabilities of the steering-based criterion with those of traditional entanglement witnesses under realistic measurement errors. The results show that the steering-based approach offers improved sensitivity for detecting weak entanglement. We further experimentally verify the feasibility of this steering-based criterion using a linear optical setup. The experimental results align well with theoretical predictions, confirming the practicality and reliability of the method. These findings establish the steering-based criterion as a promising and accessible tool for weak entanglement detection, with potential applications in quantum communication, quantum computing, and other areas of quantum information science.
  • 图 1  基于量子导引与基于纠缠目击者的量子纠缠判据比较. (I)为基于量子导引和基于纠缠目击者两种判据都可以检测到量子纠缠的区域; (II)为基于量子导引判据可以检测到量子纠缠的区域, 此区域基于纠缠目击者判据无法检测出量子纠缠; (III)为两种判据都无法检测出量子纠缠的区域. $ \gamma $为纠缠程度参数, $ \delta $为测量精度参数.

    Fig. 1.  Comparison of quantum entanglement criteria based on quantum steering and entanglement witnesses. (I) Represents the region where both quantum steering-based and entanglement witness-based criteria can detect quantum entanglement; (II) Denotes the region where entanglement can be detected by the quantum steering-based criterion but not by the entanglement witness-based criterion; (III) Indicates the region where neither criterion can detect quantum entanglement. $ \gamma $ is the entanglement strength parameter, and $ \delta $ is the measurement precision parameter.

    图 2  两光子非对称纠缠态制备与测量装置示意图

    Fig. 2.  Schematic Diagram of the Experimental Setup for Preparing and Measuring Asymmetric Entangled Two-Photon States

    图 3  $ \varepsilon $设定为$ \dfrac{9\pi}{20} $时的实验结果. (a) 在基矢$ {|+\rangle, |-\rangle} $和$ {|\varepsilon\rangle, \left|\varepsilon^{\perp}\right\rangle} $下, 对光子A进行测量, 得到4个条件概率$ p_+, p_-, p_{\varepsilon}, p_{\varepsilon^{\perp}} $. 浅蓝色柱对应纠缠态$ |\psi\rangle_e $的条件概率, 橙色柱对应可分态$ |\psi\rangle_s $的条件概率. (b) 在测量光子A后, 对光子B投影到指定量子态下的投影概率为$ \{{\cal{P}} _1, {\cal{P}} _2, {\cal{P}} _3, {\cal{P}} _4\} $. 深蓝色柱对应纠缠态$ |\psi\rangle_e $的投影概率, 粉色柱对应$ |\psi\rangle_s $的投影概率.

    Fig. 3.  The experimental results when $\varepsilon $ is set to $ \dfrac{9\pi}{20} $. (a) Photon A was measured in the bases $ {|+\rangle, |-\rangle} $ and $ {|\varepsilon\rangle, \left|\varepsilon^{\perp}\right\rangle} $, producing four conditional probabilities: $ p_+, p_-, p_{\varepsilon}, p_{\varepsilon^{\perp}} $. Light blue bars correspond to the conditional probabilities of the entangled state $ |\psi\rangle_e $, while orange bars represent those of the separable state $ |\psi\rangle_s $. (b) After the measurement of photon A, photon B was projected onto specific quantum states, resulting in projection probabilities $ \{{\cal{P}} _1, {\cal{P}} _2, {\cal{P}} _3, {\cal{P}} _4\} $. Dark blue bars illustrate the projection probabilities for the entangled state $ |\psi\rangle_e $, while pink bars denote those for the separable state $ |\psi\rangle_s $.

    图 4  $ \varepsilon $设定为$ \dfrac{17\pi}{36} $时的实验结果. (a) 在基矢$ {|+\rangle, |-\rangle} $和$ {|\varepsilon\rangle, \left|\varepsilon^{\perp}\right\rangle} $下, 对光子A进行测量, 得到4个条件概率$ p_+, p_-, p_{\varepsilon}, p_{\varepsilon^{\perp}} $. 浅蓝色柱对应纠缠态$ |\psi\rangle_e $的条件概率, 橙色柱对应可分态$ |\psi\rangle_s $的条件概率. (b) 在测量光子A后, 对光子B投影到指定量子态下的投影概率为$ \{{\cal{P}} _1, {\cal{P}} _2, {\cal{P}} _3, {\cal{P}} _4\} $. 深蓝色柱对应纠缠态$ |\psi\rangle_e $的投影概率, 粉色柱对应$ |\psi\rangle_s $的投影概率

    Fig. 4.  The experimental results when $\varepsilon $ is set to $ \dfrac{17\pi}{36} $.(a) Photon A was measured in the bases $ {|+\rangle, |-\rangle} $ and $ {|\varepsilon\rangle, \left|\varepsilon^{\perp}\right\rangle} $, producing four conditional probabilities: $ p_+, p_-, p_{\varepsilon}, p_{\varepsilon^{\perp}} $. Light blue bars correspond to the conditional probabilities of the entangled state $ |\psi\rangle_e $, while orange bars represent those of the separable state $ |\psi\rangle_s $. (b) After the measurement of photon A, photon B was projected onto specific quantum states, resulting in projection probabilities $ \{{\cal{P}} _1, {\cal{P}} _2, {\cal{P}} _3, {\cal{P}} _4\} $. Dark blue bars illustrate the projection probabilities for the entangled state $ |\psi\rangle_e $, while pink bars denote those for the separable state $ |\psi\rangle_s $.

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出版历程
  • 收稿日期:  2024-11-02
  • 修回日期:  2025-03-20
  • 上网日期:  2025-04-08

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