I think that the real question that must be asked is, "What is thought?
Is thought energy and can it be captured?? I believe that though is energy and that it can be captured. Most prevalent example of this information that can be shared between people who love each other or share strong relationships. It is not a coincidence that people who work in teams "know" what team members are thinking, nor is it a coincidence that mothers can be awoken at night when tragedy may befall one of their children that may have occurred 1,000s of kilometres away.
So if thought is energy, then information cannot be destroyed!! However what is the point of information if it cannot be communicated or transferred/captured to another person?? It is like giving me a scientific journal that is written in Icelandic. However I can learn Icelandic over a decade and therefore it is possible for that information to become useful. With thought you get one shot!!! Unless we have the learn the ability to capture someone's thought, then travel at a speed faster than the speed of thought to a point where we can get a second chance to absorb and decrypt that thought, then that thought becomes as pointless as a deaf person speaking in a soundproof room.
The example of burning a book as the destruction of information is quite childish, and the use of quantum physics to reassemble the book from the resultant ash, carbon dioxide and water is ludicrous. At least you could have been a little historical and spoke of Babylonian text on a clay tablet that is smashed, or given it some modern day relevance with a computer magnetic memory passing through an intense magnetic field.
But what about the killing of a person!!! And with their death, the killing of their thoughts and ideas!!! Isn't that the basic notion and outcome of political assassination??? The destruction of ideas and thought??? But in today's world we often do not have to kill a person to kill the the thought, governments and media simply bombard us with other ideas and thoughts that are contrary to how they do not want us to think. And the thought is lost or unheard.
Information is merely thought that is recorded/captured in a manner that may be transferred to another persons consciousness at a later time. It is the original thought that is important.