\documentclass[10pt,a4paper]{article}

\usepackage{tikz}
\usepackage{blochsphere}
\begin{document}
\begin{figure}

\begin{blochsphere}[nested=false,radius=1.5 cm,tilt=15,rotation=-20]
\drawBallGrid[style={opacity=0.3}]{30}{30}


\drawGreatCircle[style={dashed}]{-60}{0}{0}
\drawGreatCircle[style={dashed}]{60}{0}{0}

\drawRotationLeft[scale=1.3,style={red}]{-60}{0}{0}{15}
\drawRotationRight[scale=1.3,style={red}]{60}{0}{0}{15}

\node at (-0.8,1.9) {\textcolor{red}{\tiny $J_{12}(t)$}};
\node at (1.1,1.8) {\textcolor{red}{\tiny $J_{23}(t)$}};

\labelLatLon{up}{90}{0};
\labelLatLon{down}{-90}{90};
\node[above] at (up) {{\tiny $\left|1\right>$ }};
\node[below] at (down) {{\tiny $\left|0\right>$}};
\labelLatLon[labelmark=false]{d}{15}{90};
\node at (d) {\color{gray}\fontsize{0.15cm}{1em}\selectfont $60^\circ$};
\labelLatLon[labelmark=false]{d2}{5}{78};
\begin{scope}[xshift=5cm]
\drawBall
\drawBallGrid[style={opacity=0.3}]{30}{30}


\drawGreatCircle[style={dashed}]{-60}{0}{0}
\drawGreatCircle[style={dashed}]{60}{0}{0}

\drawRotationLeft[scale=1.3,style={red}]{-60}{0}{0}{15}
\drawRotationRight[scale=1.3,style={red}]{60}{0}{0}{15}

\node at (-0.8,1.9) {\textcolor{red}{\tiny $J_{12}(t)$}};
\node at (1.1,1.8) {\textcolor{red}{\tiny $J_{23}(t)$}};

\labelLatLon{up}{90}{0};
\labelLatLon{down}{-90}{90};
\node[above] at (up) {{\tiny $\left|1\right>$ }};
\node[below] at (down) {{\tiny $\left|0\right>$}};
\labelLatLon[labelmark=false]{d}{15}{90};
\node at (d) {\color{gray}\fontsize{0.15cm}{1em}\selectfont $60^\circ$};
\labelLatLon[labelmark=false]{d2}{5}{78};
\end{scope}
\end{blochsphere}

\end{figure}
\end{document}