Section "1.3.1. JSF example" provide an example of a class Login, that saves in its state an EntityManager reference and two Parameter references.

The JPA specification does not say that a Parameter instance is serializable.

This is also true for the EntityManager reference which is @Dependent (see section "1.3.3. Java EE component environment example"). JPA does not specify that the EntityManager is serializable and the EJB specification only specifies serialization semantics for passivation-enabled @Stateful EJB:s (which encourages the bean provider to not mark an EntityManager reference as transient, see EJB §4.2.1).