Both tables can have only one record on either side of the relationship. Each primary key value relates to only one record (or no records) in the related table. Keep in mind that this kind of relationship is not very common and most one-to-one relationships are forced by business rules and don't flow naturally from the data. In the absence of such a rule, you can usually combine both tables into one table without breaking any normalization rules.
There is a my article that explains how can use one to one relationship and zero relstionship using Entity Framework code first approach.
Relationship in Entity Framework Using Code First Approach With Fluent API