Imagine a war between Sri Lanka and Pakistan (perhaps over a piece of land in between). Only Pakistan has nuclear arms, not Sri Lanka.
Can deterrence exist between the two? It is easier to answer this question if you ask if deterrence can break down.
Can Sri Lanka break deterrence? No. because it has no nukes.
Can Pakistan break deterrence. Yes because it has nukes. Technically there is no way in which Sri Lanka can punish Pakistan, should Pakistan choose to use nukes against Sri Lanka. Deterrence in this case is totally one sided. Pakistan has to voluntarily choose not to use nukes, and as long as Pakistan voluntarily chooses not to use nukes "Deterrence" can be said to hold.
So deterrence itself can be defined as the non use of nuclear weapons by a state armed with nuclear weapons.
Now it is a commonly stated belief that "Mutually Assured Destruction" (MAD) was the reason why the US and USSR never fought a nuclear war. The story that is told over and over again is that if either the US or the USSR started a war that was suspected of being a nuclear strike, the other nation would launch a massive retaliation to devastate the entire opposing nation. It seems to be generally believed that deterrence between the US and USSR held ONLY because each was assured of TOTAL "assured" destruction, many times over. The suggestion here is that deterrence would not have held if the US was only half-destroyed or 1/3rd destroyed.
But that belief is patently untrue because the US itself (under Kennedy IIRC - I may have the wrong name here) is on record as deciding NOT to start a nuclear war (pre-emptive strike) against the USSR because even with overwhelming nuclear superiority over the USSR the US could not be reassured that the USSR would not be able to strike back. This was back in an era when the US had far many more nukes than the USSR.
That means the US was deterred even before the era of MAD. After the Soviet Union caught up in the numbers game the question of the US initiating nuclear war did not arise because the US was already deterred.
So why did the USSR not start a nuclear war? Especially in the early days the US did not have as many weapons as it would take to devastate the whole USSR. Whatever the reason - whether it was "voluntary" or whether it was fear of destruction by the US, the USSR was deterred. And the USSR was deterred even in the era before MAD. MAD came later and the cold war ended in that state. Again the USSR it appears was deterred by something less than total destruction.
Although both the US and the USSR were deterring each other before the era of MAD, they kept on building nuclear weapons in numbers sufficient to destroy each other many times over. But that fact is forgotten when people say that it was MAD that caused deterrence. Deterrence existed long before MAD and that deterrence was a fear of severe damage, not even total destruction. The message is clear:
A threat of total destruction of the other side was not necessary to deter the US and the USSR. Both deterred each other for years before each acquired the ability to totally destroy the other.
So I would say two things:
1) Total destruction of the other side is not a necessary condition for deterrence even if it is considered desirable.
2) A voluntary decision not to start a nuclear war by a nuclear armed nation is a necessary condition for deterrence.
JMT.
Over to you - you know who..it's for you to bite 