A lower bound on expected communication cost of quantum state redistribution

TL;DR

This paper establishes a fundamental lower bound on the expected communication cost for quantum state redistribution protocols, showing that they cannot significantly outperform worst-case costs, unlike classical protocols.

Contribution

It provides the first lower bound on expected communication cost for quantum state redistribution, highlighting fundamental differences from classical communication protocols.

Findings

Expected communication cost is not significantly better than worst-case cost

Lower bounds are independent of the number of rounds

Results contrast with classical communication protocols

Abstract

We show a lower bound on expected communication cost of interactive entanglement assisted quantum state redistribution protocols and a slightly better lower bound for its special case, quantum state transfer. Our bound implies that the expected communication cost of interactive protocols is not significantly better than worst case communication cost, in terms of scaling of error. Furthermore, the bound is independent of the number of rounds. This is in contrast with the classical case, where protocols with expected communication cost significantly better than worst case communication cost are known.