Vamsi Krishna Devabathini

We show new bounds on the quantum communication cost of single-shot entanglementassisted one-way quantum communication protocols for the quantum state redistribution task and for the sub-tasks quantum state splitting and 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 convex-split lemma which may be of independent interest. This differs from other achievability bounds for quantum state redistribution and quantum state merging , which use decoupling by application of random unitary. Convex-split lemma is based on the fact that in a one-way quantum communication protocol, measurement by Alice leads to an ensemble of states on registers owned by Bob and Referee, convex combination of which is the original mixed state shared between Bob and Referee. Through convex-split lemma, we design one such ensemble of states and use it to construct a protocol for the task of quantum state redistribution.