Near optimal bounds on quantum communication complexity of single-shot quantum state redistribution

We show near optimal bounds on the worst case quantum communication of single-shot entanglement-assisted one-way quantum communication protocols for the {\em quantum state redistribution} task and for the sub-tasks {\em quantum state splitting} and {\em quantum state merging}. Our bounds are tighter than previously known best bounds for the latter two sub-tasks. A key technical tool that we use is a {\em convex-split} lemma which may be of independent interest.

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