The Communication Value of a Quantum Channel

There are various ways to quantify the communication capabilities of a quantum channel. In this work we introduce the communication value (cv) of quantum channel, which describes the optimal probability of guessing the channel input from its output. By connecting to prior work on zero-error channel simulation, we show that the cv and its entanglement-assisted variant also offer dual interpretations as the classical communication cost for perfectly simulating different aspects of a channel using non-signaling resources. Our study involves characterizing the communication value as a generalized conditional min-entropy over the cone of separable operators. Using this characterization, we evaluate the cv for all qubit channels and higher-dimensional channels with certain symmetries. We find that the any entanglement-breaking channel has multiplicative cv when used in parallel with any other channel; the same is shown to hold for Pauli channels and partially depolarizing channels. In contrast, the cv is found to be non-multiplicative for a subset of the well-known Werner-Holevo channels. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT).

Automated summary

This work introduces the communication value (cv) of a quantum channel, which quantifies the optimal probability of guessing the input from the output. It shows that the cv offers dual interpretations as the classical communication cost for simulating different aspects of the channel. Characterizing the cv as a generalized conditional min-entropy, the study evaluates the cv for various qubit channels and channels with symmetries. It finds that certain channels have multiplicative cv when used in parallel, while others do not. The work also investigates relaxations of the channel cv to other cones such as the set of operators with a positive partial transpose.