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We show a lower bound on expected communication cost of interactiveentanglement assisted quantum state redistribution protocols and a slightlybetter lower bound for its special case, quantum state transfer. Our boundimplies that the expected communication cost of interactive protocols is notsignificantly better than worst case communication cost, in terms of scaling oferror. Furthermore, the bound is independent of the number of rounds. This isin contrast with the classical case, where protocols with expectedcommunication cost significantly better than worst case communication cost areknown.

A lower bound on expected communication cost of quantum state redistribution