How to introduce multi-column constraint with JPA annotations?

As already answered, multi-column index can be added using @Table annotation. However, columnNames needs to be the name of actual DB columns, not the class attribute. So, if the column is like the following:

@Column(name="product_id")
Long productId;

Then the @Table annotation should be like the following

@Table(uniqueConstraints=
       @UniqueConstraint(columnNames = {"product_id", "serial"})) 

You can declare unique constraints using the @Table(uniqueConstraints = ...) annotation in your entity class, i.e.

@Entity
@Table(uniqueConstraints={
    @UniqueConstraint(columnNames = {"productId", "serial"})
}) 
public class InventoryItem {
    ...
}

Note that this does not magically create the unique constraint in the database, you still need a DDL for it to be created. But seems like you are using some sort of automated tool for creating the database based on JPA entity definitions.