Is "They have unique index" Ok?

I am not sure that "They have unique index" or "They have unique indexes". It looks like "indexes" for consistency with "they", but "unique" implies it is singular. I need help on this. Thanks.

Can you share the context? The verb "have" does not need to match. e.g. I have many children. My children have a trampoline.

So "They have unique indices" or "They have a unique index" would both be fine. "They have unique index" does not work - it needs the indefinite article.

This could change a little depending on the exact context of what you're trying to say.

Edit: To be clearer, you might say "They each have a unique index."