An upper bound on the second order asymptotic expansion for the quantum communication cost of state redistribution

TL;DR

This paper establishes an upper bound on the second order asymptotic expansion for the quantum communication cost in state redistribution, advancing understanding of quantum information transfer efficiency.

Contribution

It introduces a novel upper bound on the second order asymptotic expansion for quantum communication cost in state redistribution, including a one-shot setting analysis.

Findings

Derived an upper bound on second order asymptotic expansion.

Provided an upper bound in the one-shot setting.

Utilized coherent state merging as a primitive.

Abstract

State redistribution is the protocol in which, given an arbitrary tripartite quantum state, with two of the subsystems initially being with Alice and one being with Bob, the goal is for Alice to send one of her subsystems to Bob, possibly with the help of prior shared entanglement. We derive an upper bound on the second order asymptotic expansion for the quantum communication cost of achieving state redistribution with a given finite accuracy. In proving our result, we also obtain an upper bound on the quantum communication cost of this protocol in the one-shot setting, by using the protocol of coherent state merging as a primitive.