Quantum message compression with applications

TL;DR

This paper introduces a new quantum message compression scheme using the convex split lemma, improving bounds on quantum communication costs and proposing efficient teleportation protocols with practical advantages.

Contribution

It develops the convex split lemma for quantum compression, providing tighter bounds and explicit protocols for quantum state redistribution, splitting, merging, and port-based teleportation.

Findings

Tight bounds on quantum communication costs for key tasks.

Explicit protocols outperform previous random unitaries methods.

Port-based teleportation with reduced resource requirements.

Abstract

We present a new scheme for the compression of one-way quantum messages, in the setting of coherent entanglement assisted quantum communication. For this, we present a new technical tool that we call the convex split lemma, which is inspired by the classical compression schemes that use rejection sampling procedure. As a consequence, we show new bounds on the quantum communication cost of single-shot entanglement-assisted one-way quantum state redistribution task and for the sub-tasks quantum state splitting and quantum state merging. Our upper and lower bounds are tight up to a constant and hence stronger than previously known best bounds for above tasks. Our protocols use explicit quantum operations on the sides of Alice and Bob, which are different from the decoupling by random unitaries approach used in previous works. As another application, we present a port-based teleportation scheme which works when the set of input states is restricted to a known ensemble, hence potentially saving the number of required ports. Furthermore, in case of no prior knowledge about the set of input states, our average success fidelity matches the known average success fidelity, providing a new port-based teleportation scheme with similar performance as appears in literature.