Thank you for your reply.
If you were arrested/convicted, the applicant must provide the court record from this. However, The United States does not have access to the Police National Computer, meaning they are unlikely to know about it (the information sharing with Greece/Turkey is even worse). The consulate can do an individual request to the PNC, but that rarely happens.
So let us one decides to disclose. You are ineligible to travel under the visa waiver permit if you have ever violated any law related to possessing, using or distributing illegal drugs. Meaning, you'd need to apply for a visa ahead of time with the US Consulate. You would also need to file an I-192 - a waiver requesting admissibility. If you are inadmissible due to having committed a crime involving moral turpitude (which a drug smuggling conviction is), you are eligible to apply for a waiver of waiver of ineligibility under Section 212(h) of the Immigration and Nationality Act if you can establish that: (a) The activities for which you are excluded occurred more than 15 years before the date of your application for a visa; (b) Your admission to the US would not be contrary to the national welfare, safety, or security, and (c) You have been rehabilitated. Then, the consular agent basically makes a discretionary decision.
Let us say one decides not to disclose and the consular agent never finds out. Okay, then likely visa is granted assuming no other issues pop up.
Let us say that one decides not to disclose and the consular agent finds out by an inquest to the Police National Computer on a hunch, or by better communication with Greece/Turkey (specific communication structures are not public information so it is hard to say how exactly and to which extent the countries discuss visa applicants). If so, then you would be caught in a lie and the visa denied. Furthermore, you'd likely be facing a permanent ban from the US for the incident of non-disclosure.
I normally go off the rule that being honest is the best policy, but of course, this is your decision.
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