How to pass const pointer to const object using unique_ptr

I want to pass a unique_ptr to a helper function, and I want to make sure that the helper function neither modifies the pointer, nor the pointed object. Without the unique_ptr, the solution is to have

void takePtr(AClass const * const aPtr) {
  // Do something with *aPtr. 
  // We cannot change aPtr, not *aPtr. 
}

(Well, technically, AClass const * aPtr is enough.) And I can call this with

AClass * aPtr2 = new AClass(3);
takePtr(aPtr2);

I want to instead use unique_ptr, but cannot figure out how to write this. I tried

void takeUniquePtr(unique_ptr<AClass const> const & aPtr) {
  // Access *aPtr, but should not be able to change aPtr, or *aPtr. 
}

When I call this with

unique_ptr<AClass> aPtr(new AClass(3));
takeUniquePtr(aPtr);

it does not compile. The error I see is

testcpp/hello_world.cpp:141:21: error: invalid user-defined conversion from ‘std::unique_ptr<AClass>’ to ‘const std::unique_ptr<const AClass>&’ [-fpermissive]

Shouldn't the conversion from unique_ptr<AClass> to unique_ptr<AClass const> be automatic? What am I missing here?

By the way, if I change unique_ptr<AClass const> const & aPtr to unique_ptr<AClass> const & aPtr in the function definition, it compiles, but then I can call functions like aPtr->changeAClass(), which I don't want to allow.