Quantum Channel Simulation in Fidelity is no more difficult than State Splitting

TL;DR

This paper demonstrates that simulating quantum channels in terms of fidelity can be simplified by using quantum state splitting, avoiding complex reduction techniques, and provides tighter bounds and a simpler proof of the quantum reverse Shannon theorem.

Contribution

It introduces a direct method for quantum channel simulation via state splitting, bypassing de Finetti reduction, and offers improved one-shot bounds and a simplified proof of the reverse Shannon theorem.

Findings

Quantum channel simulation in fidelity can be achieved via state splitting.

The paper provides tighter one-shot bounds for the simulation.

It simplifies the proof of the quantum reverse Shannon theorem.

Abstract

Characterizing the minimal communication needed for the quantum channel simulation is a fundamental task in the quantum information theory. In this paper, we show that, in fidelity, the quantum channel simulation can be directly achieved via quantum state splitting without using a technique known as the de~Finetti reduction, and thus provide a pair of tighter one-shot bounds. Using the bounds, we also recover the quantum reverse Shannon theorem in a much simpler way.