Antigen Lateral Flow Tests (LFTs) directly detect a protein that is contained inside the virus particle. The more virus there is, the easier it is for an LFT to detect this protein. But that means that when you are newly infected and the virus is just starting to multiply inside your body, an LFT test may fail to detect the low levels of virus present. This might happen (particularly) before you have any symptoms.
But LFTs are useful for identifying those people who are already infectious, probably symptomatic, and so have a large amount of virus in their system. RT-qPCR, which is simplified to PCR (Polymerase Chain Reaction), is more sensitive, because it makes copies of the genetic material of the virus, and even very small amounts of the genetic material will trigger an ‘exponential’ duplication: it is a ‘chain reaction’, a bit like the detonation of an atom bomb!
Consequently, PCR is so sensitive it can identify newly infected people more certainly than LFT, before they become symptomatic and before they become infectious to others. PCR is also more ‘specific’ than LFT. LFT can fail to distinguish between the SARS-CoV-2 (Covid-19) virus and other related coronaviruses. Some common colds are caused by non-SARS-CoV-2 coronaviruses, and there is potential for a lower specificity to confuse LFT and generate a false positive.
This is much less likely with PCR, which remains the diagnostic gold standard. Air travel is obviously a high risk for becoming infected. We believe that relying on the result of an LFT immediately after travelling on an aircraft is questionable: LFT is unlikely to identify anyone who has become newly infected. Even RT-qPCR would be challenged by someone very newly infected, but it is likely to identify the newly infected before LFT, due to its higher sensitivity.