Communication complexity of channels in general probabilistic theories

Area of Science:

• Quantum Information Theory
• Classical Communication Complexity
• General Probabilistic Theories

Background:

• The communication complexity of quantum channels quantifies the classical information needed to simulate quantum state preparation, transmission, and measurement.
• Current knowledge regarding this quantity is limited, hindering advancements in quantum information processing and simulation.

Purpose of the Study:

• To introduce a systematic procedure for evaluating the communication complexity of quantum channels within general probabilistic theories.
• To develop constructive methods for deriving the most efficient classical simulation protocols.

Main Methods:

• The study presents a novel, constructive procedure applicable to any general probabilistic theory, including quantum theory.
• The procedure is demonstrated by evaluating the communication complexity for a specific case: a quantum depolarizing channel with finite sets of states and measurements.

Main Results:

• A generalizable procedure for calculating quantum channel communication complexity has been established.
• The procedure yields the most efficient classical protocols for simulating the described quantum processes.
• The communication complexity of a quantum depolarizing channel was successfully evaluated using the developed method.

Conclusions:

• The developed procedure offers a powerful tool for understanding and quantifying the classical resources required for quantum simulations.
• This work advances the field of quantum information theory by providing a systematic approach to a fundamental quantity.
• The findings pave the way for more efficient classical simulations of quantum phenomena.