For a logic gate to be universal, must it necessarily be able to perform duplication?
I'm not sure what you're asking, precisely, but it's certainly not true that a reversible universal gate requires the number of set bits in the output to be the same as in the input. Toffoli gates do not have that property, for example.
EDIT
Thanks for the clarification. The answer to your question is that any reversible circuit must have at least as many output lines as input lines. As an exercise, prove this. Try using the pigeonhole principle.
So what happens if you need a reversible circuit with fewer output lines than input lines? You just add output lines, the values of which are irrelevant. The circuit still computes what you need it to, it also happens to compute more stuff that you don't care about.
So what I think you're asking about duplication is can there be more output bits than input bits? The answer is &quot;kind of&quot;, and it comes down to what model of reversibility you care about.
Such a circuit can clearly be logically reversible. But can it be physically reversible? I'm not a hardware designer, and I don't know.