Removing space between latex arrows when they have added color

Question

I want these two lines to align properly, \textcolor arrow adds extra space

\begin{align}
    \ket{\rm P}_t =& 
    \ket{\uparrow\textcolor{red}{\uparrow}\uparrow} \\ \nonumber &
    \ket{\uparrow\uparrow\uparrow}
\end{align}

Answer 1

Three Rel atoms behaves like three Ord atoms: there is no spaces between them. This is case of your second line. But the construction \textcolor{red}{\uparrow} creates Ord atom, so you have a triple Rel Ord Rel and TeX inserts spaces between them. But you can re-type Rel atoms to Ord by encapsulating them to {...}, so your desired behavior can be reached by:

\ket{{\uparrow}\textcolor{red}{\uparrow}{\uparrow}} \\ \nonumber &

Answer 2

In the “all black” case you're being lucky, because \uparrow is defined as a relation symbol and TeX adds

• no space between an opening delimiter and a relation symbol;
• no space between relation symbols;
• no space between a relation symbol and a closing delimiter.

In the colored case, the middle arrow is treated as an ordinary symbol and TeX adds a thick space between a relation symbol and an ordinary one, in either order.

Solution. Define a command for an up arrow to be considered as an ordinary symbol: all it takes is to brace \uparrow. You can also add an optional argument for the color.

This requires an up-to-date TeX distribution:

\documentclass{article}
\usepackage{amsmath}
\usepackage{braket}
\usepackage{xcolor}

\NewDocumentCommand{\xuparrow}{o}{{%
  \IfNoValueTF{#1}{\uparrow}{\mathcolor{#1}{\uparrow}}%
}}

\begin{document}

\[
\ket{\mathrm{P}_t} = 
\ket{\xuparrow\xuparrow[red]\xuparrow}
\]

\end{document}

For older LaTeX versions you can resort to

\documentclass{article}
\usepackage{amsmath}
\usepackage{braket}
\usepackage{xcolor}

\newcommand{\xuparrow}[1][]{{%
  \if\relax\detokenize{#1}\relax
    \uparrow
  \else
    \textcolor{#1}{\uparrow}%
  \fi
}

\begin{document}

\[
\ket{\mathrm{P}_t} = 
\ket{\xuparrow\xuparrow[red]\xuparrow}
\]

\end{document}

Choose a more descriptive name for the command, based on its meaning.

Also note that \rm has been deprecated for almost 30 years.

Answer 3

A very simple solution would be to wrap the correspondent black arrow inside curly brackets. Arrows are properly aligned, but not necessarily the alignment you want. I removed \ket since I don't know from which package it comes from.

\documentclass{article}
\usepackage{amsmath,xcolor}
\begin{document}
\begin{align}
  a & = \uparrow\textcolor{red}{\uparrow}\uparrow \\
  b & = \uparrow{\uparrow}\uparrow
\end{align}
\end{document}