Well, I added

  <policy domain="coder" rights="read | write" pattern="PDF" />

just before </policymap> in /etc/ImageMagick-7/policy.xml and that makes it work again, but not sure about the security implications of that.

As pointed out in some comments, you need to edit the policies of ImageMagick in /etc/ImageMagick-7/policy.xml. More particularly, in ArchLinux at the time of writing (05/01/2019) the following line is uncommented:

<policy domain="coder" rights="none" pattern="{PS,PS2,PS3,EPS,PDF,XPS}" />

Just wrap it between <!-- and --> to comment it, and pdf conversion should work again.

For me on my archlinux system the line was already uncommented. I had to replace "none" by "read | write " to make it work.

For me on Arch Linux, I had to comment this:

  <policy domain="delegate" rights="none" pattern="gs" />

On Ubuntu 19.10, I have done this in /etc/ImageMagick-6/policy.xml

uncomment this

<policy domain="module" rights="read | write" pattern="{PS,PDF,XPS}" />

and comment this

<!-- <policy domain="coder" rights="none" pattern="PDF" /> -->

After that, this command work without error

convert -thumbnail x300 -background white -alpha remove sample.pdf sample.png 

I was experiencing this issue with nextcloud which would fail to create thumbnails for pdf files.

However, none of the suggested steps would solve the issue for me.

Eventually I found the reason: The accepted answer did work but I had to also restart php-fpm after editing the policy.xml file:

 sudo systemctl restart php7.2-fpm.service

This issue is a workaround for a security vulnerability. The vulnerability has been addressed in Ghostscript 9.24 (source), so if you have that or a newer version, you don't need the workaround anymore.

On Ubuntu 19.10 through 21.04 and probably any later versions coming with ImageMagick 6, here's how you fix the issue by removing the workaround:

1. Make sure you have Ghostscript ≥9.24:

   gs --version
   

2. If yes, just remove this whole following section from /etc/ImageMagick-6/policy.xml:

   <!-- disable ghostscript format types -->
   <policy domain="coder" rights="none" pattern="PS" />
   <policy domain="coder" rights="none" pattern="PS2" />
   <policy domain="coder" rights="none" pattern="PS3" />
   <policy domain="coder" rights="none" pattern="EPS" />
   <policy domain="coder" rights="none" pattern="PDF" />
   <policy domain="coder" rights="none" pattern="XPS" />
   

Works in Ubuntu 20.04

Add this line inside <policymap>

<policy domain="module" rights="read|write" pattern="{PS,PDF,XPS}" />

Comment these lines:

  <!--
  <policy domain="coder" rights="none" pattern="PS" />
  <policy domain="coder" rights="none" pattern="PS2" />
  <policy domain="coder" rights="none" pattern="PS3" />
  <policy domain="coder" rights="none" pattern="EPS" />
  <policy domain="coder" rights="none" pattern="PDF" />
  <policy domain="coder" rights="none" pattern="XPS" />
   -->

Adding to Stefan Seidel's answer.

Well, at least in Ubuntu 20.04.2 LTS or maybe in other versions you can't really edit the policy.xml file directly in a GUI way. Here is a terminal way to edit it.

1. Open the policy.xml file in terminal by entering this command -

   sudo nano /etc/ImageMagick-6/policy.xml

2. Now, directly edit the file in terminal, find <policy domain="coder" rights="none" pattern="PDF" /> and replace none with read|write as shown in the picture. Then press Ctrl+X to exit.

The ImageMagick change was kept after Ghostscript was fixed because applications (especially web applications) often feed arbitrary user-supplied files to ImageMagick, don't always enforce format restrictions properly, and, since Postscript (which PDF uses) is a turing-complete programming language running in a sandbox, there's always the possibility of another hole in the sandbox.

It's much better to leave things configured so ImageMagick refuses to process files that require running a program and, instead, just invoke Ghostscript directly when you intentionally want to permit Postscript rendering.

That would be accomplished by a Ghostscript command like this:

gs -dSAFER -r600 -sDEVICE=pngalpha -o foo.png myfile.pdf

Yes, this is a variation on the GhostScript command ImageMagic calls. (see ImageMagick's delegates.xml. -o is shorthand for -dBATCH -dNOPAUSE -sOutputFile=)

What's important is that ImageMagick stays locked down, you don't needlessly invoke an intermediate program, and you get more control over the rendering parameters. (eg. -r600 is the DPI to render at and changing -sDEVICE=pngalpha allows you to render directly to your desired format)

Manjaro April 2021

Just remove uncommented line inside <policymap> in /etc/ImageMagick-7/policy.xml

As a highly active comment by @Richard Kiefer, a simple fix is like this

$ sudo sed -i '/disable ghostscript format types/,+6d' /etc/ImageMagick-6/policy.xml

In my case i'm useing ubuntu 20.10 and the Imagick-7.

in my /etc/ImageMagick-6/policy.xml I've removed below lines, restarted my machine and I'm done.

  <policy domain="coder" rights="none" pattern="PS" />
  <policy domain="coder" rights="none" pattern="PS2" />
  <policy domain="coder" rights="none" pattern="PS3" />
  <policy domain="coder" rights="none" pattern="EPS" />
  <policy domain="coder" rights="none" pattern="PDF" />
  <policy domain="coder" rights="none" pattern="XPS" />