a 'minimum security prison' [=a prison in which prisoners are allowed more freedom than in most other prisons because they are not considered dangerous or likely to escape]
Ten years is the 'minimum' needed. = We'll need 10 years 'at a/the minimum'. [=we'll need at least 10 years]
We need to keep expenses 'to a (bare) minimum'. [=we need to keep expenses as low as possible]
(..) I know how smart you are. You're just telling me what I want to hear. I don't think you believe what you're telling me. If I put you in minimum security you'll just try to escape again. You have to let me see my son. Please. Please. He's in great danger. (..)1991 Terminator 2: Judgment Day
(..) something to look forward to. And what is that? You said that if I showed improvement after six months, you would transfer me to the minimum security wing and l could have visitors. Well, it's been six months. I was looking forward to seeing my son. I see. (..)1991 Terminator 2: Judgment Day