赤道平面与布洛赫球面的交点

Question

我已经创建了一个Bloch sphere我想显示赤道平面与球体的交点。我尝试了以下方法，但我相信还有改进的空间。

\documentclass[border=5pt]{standalone}
\usepackage{blochsphere}
\usepackage{tikz-3dplot}
\begin{document}
  \begin{blochsphere}[radius = 1.5 cm, tilt = 15, rotation = -45, opacity = 0.20]
    % Drawing the equatorial plane
    \tdplotsetmaincoords{5}{0}
    \tdplotsetrotatedcoords{0}{0}{0}
    \begin{scope}[tdplot_rotated_coords]
      \draw[fill=blue,opacity=0.2, scale=3] (-0.5,0,-0.5) -- (-1,0,1) -- (1,0,1) -- (0.5,0,-1) -- cycle;
    \end{scope}
    % Draw the ball and grid
    \drawBallGrid[style={opacity=0.5, color = blue, loosely dashed}]{180}{180}
    % Axes (X, Y, Z)
    \drawStatePolar[axisarrow = true, statewidth = 0.5, scale = 1.50]{x}{90}{90}
    \drawStatePolar[axisarrow = true, statewidth = 0.5, scale = 1.50]{y}{90}{00}
    \drawStatePolar[axisarrow = true, statewidth = 0.5, scale = 1.15]{z}{00}{00}
    \end{blochsphere}
\end{document}

Answer 1

我认为您希望tikz-3dplot与 结合使用blochsphere。这些包有不同的方法来设置视角。因此，需要调整 中的 theta 角度tikz-3dplot以匹配 使用的投影blochsphere。

\documentclass[border=5pt]{standalone}
\usepackage{blochsphere}
\usepackage{tikz-3dplot}
\begin{document}
  \begin{blochsphere}[radius = 1.5 cm, tilt = 15, rotation = -45, opacity = 0.20]
    % Drawing the equatorial plane
    \tdplotsetmaincoords{105}{45}
    \tdplotsetrotatedcoords{0}{0}{0}
    \begin{scope}[tdplot_main_coords,canvas is xy plane at z=0,on layer=back]
      \fill[blue!40,opacity=0.5] (-6,-6) -- (225:1.5) arc(225:45:1.5)
      -- (6,6) -- (6,-6) --cycle;
    \end{scope}
    % Draw the ball and grid
    \drawBallGrid[style={opacity=0.5, color = blue, loosely dashed}]{180}{180}
    % Axes (X, Y, Z)
    \drawStatePolar[axisarrow = true, statewidth = 0.5, scale = 1.50]{x}{90}{90}
    \drawStatePolar[axisarrow = true, statewidth = 0.5, scale = 1.50]{y}{90}{00}
    \drawStatePolar[axisarrow = true, statewidth = 0.5, scale = 1.15]{z}{00}{00}
    \begin{scope}[tdplot_main_coords,canvas is xy plane at z=0,on layer=front]
      \fill[blue!40,opacity=0.5] (-6,-6) -- (225:1.5) arc(225:45:1.5)
      -- (6,6) -- (-6,6) --cycle;
    \end{scope}
\end{blochsphere}
\end{document}