a third party can voluntarily surrender complete control over what is going on. they can issue a token for something, for example a $10 dollar bill but do it in such a way (blind signature) that when you go to spend it they cannot connect the spend to the bill they issued.

if you want to do it without a third party you end up with something like zcash. monero plans to follow suit (currently only the amounts in monero are zero knowledge).

That can leak information to the third party that you may not want them to know.

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You can. For example for verifying enough funds the immigration office could ask the bank itself. But it also adds additional problem, such that without users concern they can do anything. Even if it’s solved with papers and users signature it’s more slower. With zk proof you can optimize immigration from third world country to the first world country with a single online application.

Or you can make it for remote programming job. Create a zk proof of codes he has worked on. And apply to HR so hr doesnt have to waste time on due diligence or mess with nda to look at private code base, few devs have public code. Zk makes, cross institute as an online service more efficient.