Communication Complexity of Channels in General Probabilistic Theories

TL;DR

This paper introduces a systematic method to evaluate the classical communication complexity of channels within general probabilistic theories, including quantum channels, providing efficient simulation protocols.

Contribution

It presents a constructive procedure to compute the communication complexity of channels in any probabilistic theory, improving understanding and simulation efficiency.

Findings

Evaluated the communication complexity of a quantum depolarizing channel.

Provided the most efficient classical protocols for channel simulation.

Applicable to general probabilistic theories, including quantum mechanics.

Abstract

The communication complexity of a quantum channel is the minimal amount of classical communication required for classically simulating the process of preparation, transmission through the channel, and subsequent measurement of a quantum state. At present, only little is known about this quantity. In this paper, we present a procedure for systematically evaluating the communication complexity of channels in any general probabilistic theory, in particular quantum theory. The procedure is constructive and provides the most efficient classical protocols. We illustrate this procedure by evaluating the communication complexity of a quantum depolarizing channel with some finite sets of quantum states and measurements.