The scenario you are describing here isn't really ideal. This isn't really a restriction on Entity Framework; it's more a restriction on the database stack. By default, the Id primary key is an Identity column, and SQL itself isn't really supportive of the idea of "shared" Identity columns. You can disable Identity and manage the Id properties yourself, but then Entity Framework cannot automatically build navigation properties for your entities.
The best option here is to use one single participant table, in a technique called "Table Per Hierarchy", or TPH. Entity Framework can manage the single table using an internal discriminator column. Shared properties can be put into the base class, and non-shared properties can be put on the individual classes, which Entity Framework will composite into a single large table in the DB. The main drawback to this strategy is that columns for non-shared properties will automatically be nullable in the database. This article describes this scenario very well.
The more I try to come up with a solution, I realize that this is an example of the XY Problem. There is not really a good solution to this question, because this question is already a proposed solution. There is a problem here that has led you to create an Interface which you suggest requires the entities which are using the interface to have a unique Id. This really sounds like an issue with the design of the Interface itself, as Interfaces should be agnostic to the entity they are applied to. Perhaps providing some code and showing what your problem actually is would be helpful, since the proposed solution you are asking how to implement here isn't really practical.
