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 $设定为$ {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_{\mathrm{e}} $的条件概率, 橙色柱对应可分态$ |\psi\rangle_{\mathrm{s}} $的条件概率; (b)在测量光子A后, 光子B投影到指定量子态下的投影概率为$ \{{\cal{P}} _1, {\cal{P}} _2, {\cal{P}} _3, {\cal{P}} _4\} $. 深蓝色柱对应纠缠态$ |\psi\rangle_{\mathrm{e}} $的投影概率, 粉色柱对应$ |\psi\rangle_{\mathrm{s }}$的投影概率

Fig. 3.  The experimental results when $\varepsilon $ is set to $ {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_{\mathrm{e}} $, while orange bars represent those of the separable state $ |\psi\rangle_{\mathrm{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_{\mathrm{e}} $, while pink bars denote those for the separable state $ |\psi\rangle_{\mathrm{s}} $.

图 4  $ \varepsilon $设定为$ {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_{\mathrm{e}} $的条件概率, 橙色柱对应可分态$ |\psi\rangle_{\mathrm{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_{\mathrm{e}} $的投影概率, 粉色柱对应$ |\psi\rangle_{\mathrm{s}} $的投影概率

Fig. 4.  The experimental results when $\varepsilon $ is set to $ {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_{\mathrm{s}} $. (b) After the measurement of photon A, photon B is 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_{\mathrm{e }}$, while pink bars denote those for the separable state $ |\psi\rangle_{\mathrm{s}} $.