Is the prayer of one who carries a bottle of wine in his pocket valid?

The answer to this question depends on the view we take on the type of impurity we attach to all intoxicating drinks including wine. God the Almighty describes wine in the Quran as impure, but the majority of scholars consider this impurity to be figurative in the same sense as unbelievers are described as impure. Should we shake hands with an unbeliever, we do not have to wash our hands like we must do when they are defiled by an impure substance. This is because the impurity is figurative. Alcohol is impure in the same sense. As such, a person carrying a wine bottle in his pocket while praying is not carrying a physical impurity. Hence, his prayer is valid although he is committing something which is forbidden. The two actions are considered separate. On the other hand, if we consider wine to be a physical impurity as some scholars do, then the prayer is invalid because an essential condition for the validity of prayer is purity of body, clothes and place of prayer.

Having said that, there is a third way to look at this question. If the man knows the position of Islam on alcoholic drinks and still carries a bottle of wine in his pocket while praying, then his action is considered a mockery of prayer. He may be considered a hypocrite, although only God the Almighty knows what is in people's hearts.

That said, I would like to add that in the past, students of Islamic jurisprudence indulged in trying to come up with answers to hypothetical questions of this sort. Their action was not welcomed by scholars, because a scholar should concentrate on practicalities and not on hypothetical questions that may never arise.
And God the Almighty knows best.