JPA: Using @MapKey for an abstract class

I have the following structure of an abstract superclass A and a class Z referring to As sublasses B and C using a map:

@Entity
Abstract Class A
    @Id
    @GeneratedValue(strategy = GenerationType.AUTO)
    private long id;
    Integer map_field; <----------------------- Problematic
    ....

@Entity
Class B extends A
    @Id
    @GeneratedValue(strategy = GenerationType.AUTO)
    private long id;
    Integer map_field;
    ....

@Entity
Class C extends A
    @Id
    @GeneratedValue(strategy = GenerationType.AUTO)
    private long id;
    Integer map_field;
    ....

@Entity
Class Z
    @Id
    @GeneratedValue(strategy = GenerationType.AUTO)
    private long id;
    @OneToMany(cascade = CascadeType.ALL)
    @MapKey(name="map_field")
    private Map<Integer,A> a_entities;

The problem is that the map_field is based on values of the objects B and C and not on class values of A.

So basically I cannot use the map_field using the @MapKey annotation in class Z as written above. I do not have useful values for the map_field of class A.

Does anyone have hints how I can solve this problem?

Thanks in advance, Alex