Fortunately for those who want to see a global ban on nuclear weapons, the process for ensuring that countries comply with such a ban is far more straightforward than for, say, chemical weapons or landmines.
Because nuclear explosions are so massive, they are very hard to hide. While it is conceivable to produce nuclear weapons without ever testing one, and Israel may have managed to do that (although they probably tested their first weapon jointly with South Africa) most countries that would want to produce a nuclear weapon would want to test it out, not only to see if it works but also to show to the world that they have one.
There is no place left on earth, under the earth or even under the sea, where a nuclear explosion would not be detected by infrared satellite imaging and/or by seismic equipment used for detected earthquakes. So it is literally impossible for a country to test a nuclear weapon without it being known. This is not something that can be said for any other type of weapon system.
To produce a working nuclear weapon also requires a delivery system of some kind – airplane, missile, mobile bomb launcher, whatever. While there may be some rather crude delivery systems available for detonating a nuclear device in situ wherever that may be, in most cases delivering a nuclear weapon requires very sophisticated missile technology, which as even the UK itself does not have (it relies on US missiles to deliver its own nuclear weapons).
Heavy bomber aircraft for delivering nuclear weapons also require a level of sophistication which most countries do not have. Once again, testing of medium or long-range missiles or aircraft is very hard to do in the modern world without detection.
By far the biggest challenge of building a nuclear weapon is not the design, which can be obtained from the internet, but obtaining the raw materials for making the bomb: either highly-enriched uranium or plutonium. The enrichment of uranium is a vastly expensive and complicated process which requires sophisticated and high precision equipment.
Plutonium can be created (it does not exist naturally) in certain designs of nuclear power station, but since civil nuclear power stations can be monitored by the IAEA it is difficult to produce plutonium undetected without withdrawing from the IAEA and sounding a warning bell to the international community as was the case with Iran.
The recent deal reached between Iran and a group of countries trying to prevent it from building a nuclear weapon is a good example of how difficult it is for any country to produce nuclear weapons without being noticed. Of course any country can choose to go ahead anyway, but there may be global consequences for doing so.
In the 1980s, following the INF Treaty which abolished all intermediate range nuclear weapons in Europe, Russian inspectors were invited onto US bases to verify withdrawal and dismantling of nuclear weapons systems and US inspectors were invited onto Soviet bases to verify the same thing on the other side.
In the case of the START Treaty which required destruction of a certain number of existing long-range nuclear bombers on both sides, the US and Russia both chopped up planes into pieces and left them spread out on the ground until satellite reconnaissance from the other side could verify that they had been destroyed.
While it is not possible to ‘uninvent’ anything, it is certainly possible to get rid of things we no longer want or need, including obsolete weapons systems. All that is needed is the political will and ways can be found to verify disarmament moves and to monitor compliance.
The reality is that most countries do not have nuclear weapons. Some have the capability to produce nuclear weapons and have chosen not to. Others have developed them or begun developing them and then decided to abandon their nuclear programmes.
Because nuclear weapons are so massive in their destructive power and require such sophisticated and expensive facilities to manufacture, their elimination is much easier than any other weapon to monitor and verify.
There will always be the possibility that an advanced industrialised country could at some point in the future manufacture nuclear weapons if they chose to. Current monitoring and verification technologies mean that it will be much more difficult for them to do so without the rest of the world finding out about it. In a world in which nuclear weapons are not acceptable under any circumstances the norm will be established in which it is less likely that any country will choose to manufacture them once they have been eliminated.