In quantum state redistribution as introduced in [Luo and Devetak (2009)] and
[Devetak and Yard (2008)], there are four systems of interest: the A system
held by Alice, the B system held by Bob, the C system that is to be
transmitted from Alice to Bob, and the R system that holds a purification of
the state in the ABC registers. We give upper and lower bounds on the amount
of quantum communication and entanglement required to perform the task of
quantum state redistribution in a one-shot setting. Our bounds are in terms of
the smooth conditional min- and max-entropy, and the smooth max-information.
The protocol for the upper bound has a clear structure, building on the work
[Oppenheim (2008)]: it decomposes the quantum state redistribution task into
two simpler quantum state merging tasks by introducing a coherent relay. In the
independent and identical (iid) asymptotic limit our bounds for the quantum
communication cost converge to the quantum conditional mutual information
I(C:R∣B), and our bounds for the total cost converge to the conditional
entropy H(C∣B). This yields an alternative proof of optimality of these rates
for quantum state redistribution in the iid asymptotic limit. In particular, we
obtain a strong converse for quantum state redistribution, which even holds
when allowing for feedback.Comment: v3: 29 pages, 1 figure, extended strong converse discussio