The Sun states that they are infallible:
It is virtually impossible to trick a lie-detector because it picks up signals of fear, which emanate from the hypothalamus gland in the neck.No, they're not!
What is the evidence regarding their accuracy? Well, the American Psychological Association (APA) states that they are no good at actually detecting whether or not someone is lying. Amongst other things there are no studies into any placebo-like effects, i.e. it is not possible to know whether the results are accurate or whether they are simply due to someone believing them to be accurate. There is also the slight problem in that it is entirely possible that a person could be telling the truth but is nervous while doing the test, which would lead to results that suggest that they are lying. Conversely, someone whom is lying may be capable of controlling their emotions, which would lead to results that would suggest that they are telling the truth.
What about the "Top US lie-detector expert" that the Sun refers to? As far as I can make out, he is a business man with an honorary qualification from the Hawaii Organization of Polygraph Examiners (who appear to have no internet presence at all...), the Texas Association Of Polygraph Examiners but he doesn't appear to be on their list of members, but the company is (but this hasn't been updated since October 2007) and the American Polygraph Association, whose membership list is currently being upgraded. He's labelled as a BS - the US name for a BSc - but it doesn't say what it is in.
So what can we say in summary? The best bet is to quote the APA
For now, although the idea of a lie detector may be comforting, the most practical advice is to remain skeptical about any conclusion wrung from a polygraph.Given the difficulties in also establishing the "expert"'s qualifications, I can only concur.
Of course, if anyone is able to find any more about the "expert", leave a comment.