Case I: Alice and Bob each have a quantum state. Their quantum states are maximally entangled.
Case II: Alice and Charlie each have a quantum state. Their quantum states are maximally entangled.
Cases I and II are not happening simultaneously.
Say each person's state was stored in a (separate) quantum memory. Alice used the same quantum memory in both cases. Is it guaranteed that given the condition of maximal entanglement, that Bob and Charlie had idenitcal quantum states in their respective quantum memories?