Here's one way to understand the difference: "Without a trace/without a single trace" - pretty much the same thing. Not a single piece of evidence could be found. Adding "single" just emphasises this. "Without trace" - again, without evidence but in the general sense. "The ship vanished without (any) trace." We're not being specific or emphatic by adding "a" or "a single", the ship simply vanished. ...and Tracy is still waiting at the dock side. She is well disappointed.

José, The expression "sunk without trace" is not that old. It is a direct translation of the German phrase "spurlos versenkt". According to the Unabridged Oxford, "The phrase became widely known as a result of the publication in 1917 of a secret telegram sent in May of that year by Count Luxburg, the German minister in Buenos Aires, to Berlin, advising that Argentine shipping should be either turned back or sunk without trace." The expression 'to sink without trace' is normally used in the figurative sense....done for; forgotten about completely; lost from sight. -Winston Churchhill in 1945, " He has departed 'spurlos versenkt' --as the German expression says-- sunk without leaving a trace behind." ------ It seems that originally the form without (a) was used in reference to the German term, -They enjoyed brief success and then sank without trace. but now the form with (a) is also used. -Since his last book five years ago he has sunk without a trace. ----- In literal use (if a ship actually sinks without leaving any traces behind) you would more likely encounter the form with (a). The ship sank without a trace.

Both are correct. However, I think that because the word 'trace' can be used as both a concrete noun and abstract noun, it can be used with and without the article 'a'. If it is used as a concrete noun (= object, something that shows that the ship existed before), therefore we should use 'a' (without a trace). If it is used just as an abstract noun (= the general sense, as Peachey stated) like in 'HE vanished without trace', therefore we can use it without 'a'. What do you think???

Most English speakers would say "without a trace"