Quantum Channel Simulation and the Channel's Smooth Max-Information

TL;DR

This paper introduces the channel's smooth max-information as a key measure for quantum channel simulation, providing operational interpretations, computational methods, and asymptotic properties that extend understanding of quantum communication limits.

Contribution

It defines the channel's smooth max-information, links it to simulation costs, and establishes its asymptotic behavior, advancing the theoretical framework of quantum channel simulation.

Findings

The simulation error and cost are characterized by semidefinite programs.

The channel's smooth max-information equals the one-shot simulation cost under no-signalling codes.

It converges to the quantum mutual information asymptotically, supporting the quantum reverse Shannon theorem.

Abstract

We study the general framework of quantum channel simulation, that is, the ability of a quantum channel to simulate another one using different classes of codes. First, we show that the minimum error of simulation and the one-shot quantum simulation cost under no-signalling assisted codes are given by semidefinite programs. Second, we introduce the channel's smooth max-information, which can be seen as a one-shot generalization of the mutual information of a quantum channel. We provide an exact operational interpretation of the channel's smooth max-information as the one-shot quantum simulation cost under no-signalling assisted codes, which significantly simplifies the study of channel simulation and provides insights and bounds for the case under entanglement-assisted codes. Third, we derive the asymptotic equipartition property of the channel's smooth max-information; i.e., it converges to the quantum mutual information of the channel in the independent and identically distributed asymptotic limit. This implies the quantum reverse Shannon theorem in the presence of no-signalling correlations. Finally, we explore the simulation cost of various quantum channels.