How can classes with `std::variant` members be copied safely?

cppreference has this to say about std::variant's copy constructor:

Copy constructor. [...] This constructor is defined as deleted unless std::is_copy_constructible_v<T_i> is true for all T_i in Types. [...]

In other words, it is not deleted unless one or more of the types that the std::variant can contain is not copyable for whatever reason. In your case, it's the std::unique_ptr that's causing the problem. Perhaps std::shared_ptr would be more appropriate.

Extending Paul Sanders' answer: what kind of copy do you want?

If it is a shallow copy, use shared_ptr<A>.

If it is a deep copy, why not have variant<..,A>? If the reason is that A is polymorphic, then the real problem is cloning each of the derived classes. You have to create your own mechanism for the cloning and your own copyable smart pointer to use it - as far as I know, there is nothing in the standard library to help you.