public interface ISomeInterface
{
    int TestProperty
    {
        // No access modifier allowed here because this is an interface.
        get;
    }
}

public class TestClass : ISomeInterface
{
    public int TestProperty
    {
        // Cannot use access modifier here because this is an interface implementation.
        get { return 10; }

        // Interface property does not have set accessor, so access modifier is allowed.
        protected set { }
    }
}