Your second function still mixes ownership with resource management. Taking an unique_ptr<BigInteger> by value means, add_one takes the ownership of it. But it does not return anything, making it a useless function.

The though-process goes like this:

* Do you need read-only access to the argument, take a const T&

* Do you need to modify the argument, take a T (by value), letting the call site decide to either pass an rvalue (move it, no copy), or an lvalue (copy)

There simply is no need for unique_ptr<BigInteger>, as BigInteger already handles its resources internally (with move semantics). It's the same reason as to why an owning pointer to a vector is silly when a vector already handles ownership of its resources.

http://klmr.me/slides/modern-cpp/#9 is exactly about this.