The fact is that we know very little about how our immune system responds to SARS CoV-2.
The US, the UK, and Germany are among the countries that are toying with the idea of having immunity passports—people who have recovered from Covid-19 and test positive for antibodies against it will be allowed to travel and commute, while others, depending on individual governments, are forced to stay home or face curtailment of movement. While the nations want to get their economies going by allowing movement of such individuals, the fact is that we know very little about how our immune system responds to SARS CoV-2 to hazard such qualified liberties for people.
There is evidence that those who have recovered from Covid-19 developed some antibodies to the SARS CoV-2 virus. But, scientists don’t know yet what the critical level of antibodies to stave off a future infection is, whether every recovered case has enough antibodies (past the critical level), or how long these antibodies shield one against the disease.
Advising caution, the WHO notes that some recovered individuals have been detected with levels of antibodies that could be considered low. Also, if the immune response to SARS CoV-2 has a SARS- or MERS-like trajectory, a recovered individual may be able to fight off the virus for a year or two. But, if SARS CoV-2 triggers an immune response similar to common-cold coronaviruses, the antibody cover could be quite short-lived. That apart, there is the matter of questionable specificity/sensitivity of most serological testing kits. Immunity passports, in a nutshell, could just as well invite more problems than they solve.