How to typeset this such that they look symmetrical?

Question

I am trying to type

$$\left|\uparrow\right\rangle_A{}_A\left\langle\uparrow\right|$$

But the As in the subscript are not symmetrical. One is upper and another is lower. Is there a way to type this more elegantly?

Answer 1

One way is to use \DeclarePairedDelimiter from mathtools package (an extension of amsmath):

\documentclass{article}
\usepackage{mathtools}

\DeclarePairedDelimiter{\ket}{\lvert}{\rangle}
\DeclarePairedDelimiter{\bra}{\langle}{\rvert}

\begin{document}
\[
\left|\uparrow\right\rangle_A{}_A\left\langle\uparrow\right|
\]

\[
\ket{\uparrow}_{A} {}_{A}\bra{\uparrow}
\]
\end{document}

Edit

For fractions or tall expressions as leftaroundabout said in the comments, mathtools provides two options: An optional parameter \ket[size command]{something} and a starred version \ket*{something} that is preceded by \left and \right so they "grow" to match the content inside.

There are more additions to de delimiters, for example \DeclarePairedDelimiterX to be able to use arguments in the definition, as a \newcommand. Some examples from the manual:

\documentclass{article}
\usepackage{mathtools}

\DeclarePairedDelimiter{\ket}{\lvert}{\rangle}
\DeclarePairedDelimiter{\bra}{\langle}{\rvert}
\DeclarePairedDelimiterX\braket[3]{\langle}{\rangle}%
 {#1\,\delimsize\vert\,\mathopen{}#2\,\delimsize\vert\,\mathopen{}#3}

\begin{document}
\[
  \bra[\Big]{\frac{a}{b}}, \quad \ket*{\frac{a}{b}}, \quad \braket*{B}{\sum_{k} f_k}{C}
\]
\end{document}

For the subindex in this taller delimiters it is still needed \prescript as in leftaroundabout answer.

Answer 2

\documentclass{article}
\usepackage{mathtools}

\begin{document}

^_% I would use \prescript:

\[
  \left|\uparrow\right\rangle_A\prescript{}{A}{\left\langle\uparrow\right|}
\]

^_% Note that this also works when the kets get taller:

\[
  \left|\frac{\uparrow}{\downarrow}\right\rangle_A
   \prescript{}{A}{\left\langle\frac{\uparrow}{\downarrow}\right|}
\]

^_% Shame about the (lack of) kerning. We might hack it to be a bit more snug with some manual spacing adjustments:

\[
  \left|\frac{\uparrow}{\downarrow}\right\rangle_{\!\!A}
   \: \prescript{}{A}{\!\left\langle\frac{\uparrow}{\downarrow}\right|}
\]

\end{document}