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Quantum Advantages of Communication Complexity from Bell Nonlocality
Zhih-Ahn Jia1,2, Lu Wei3, Yu-Chun Wu1,2
1CAS Key Laboratory of Quantum Information, School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China.
Entropy (Basel, Switzerland)
|July 2, 2021
Summary
This study introduces a novel graph-theoretic method to create communication complexity problems from Bell tests. This approach enhances problem-solving capabilities by leveraging entangled states for superior success probabilities compared to classical strategies.
Area of Science:
- Quantum Information Theory
- Foundations of Physics
Background:
- Communication complexity (CC) problems are vital for exploring physical theory limits.
- Distributed parties aim to compute functions using restricted classical communication.
Purpose of the Study:
- To develop a method for constructing communication complexity problems from Bell tests.
- To utilize graph theory for this construction.
Main Methods:
- Constructing CC problems from Bell tests using a graph-theoretic approach.
- Defining a target function from an experimental compatibility graph and Bell test function.
- Developing a CC function based on the target function.
Main Results:
- Pre-sharing entangled states allows CC functions to achieve higher success probabilities than arbitrary classical strategies.
- A non-signaling protocol using Popescu-Rohrlich boxes achieves a success probability of one.
Conclusions:
- The proposed method provides a new way to formulate and analyze communication complexity problems.
- Quantum resources, specifically entangled states, offer significant advantages in communication complexity tasks.
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