The Generalized Capacity of a Quantum Channel

TL;DR

This paper introduces a new mathematical quantity called the generalized information, unifying classical mutual information and quantum coherent information, to better characterize the capacity of quantum channels for transmitting classical and quantum data.

Contribution

It proposes the generalized information as a unified measure and defines a transmission task whose capacity is characterized by this new quantity, bridging classical and quantum channel capacities.

Findings

The generalized information encompasses classical mutual information and coherent information.

The transmission capacity of the defined task is characterized by the generalized information.

Provides a unified framework for understanding quantum channel capacities.

Abstract

The transmission of classical information over a classical channel gave rise to the classical capacity theorem with the optimal rate in terms of the classical mutual information. Despite classical information being a subset of quantum information, the rate of the quantum capacity problem is expressed in terms of the coherent information, which does not mathematically generalize the classical mutual information. Additionally, there are multiple capacity theorems with distinct formulas when dealing with transmitting information over a noisy quantum channel. This leads to the question of what constitutes a mathematically accurate quantum generalization of classical mutual information and whether there exists a quantum task that directly extends the classical capacity problem. In this paper, we address these inquiries by introducing a quantity called the generalized information, which serves as a mathematical extension encompassing both classical mutual information and coherent information. We define a transmission task, which includes as specific instances both classical information and quantum information capacity problems, and show that the transmission capacity of this task is characterized by the generalized information.