Quantum Advantage in Non-Interactive Source Simulation

Core Concepts

There is quantum advantage in non-binary output non-interactive source simulation (NISS) scenarios, but not in binary output NISS scenarios.

Abstract

The paper considers two variations of the standard non-interactive source simulation (NISS) problem:

Entanglement-Assisted NISS (EA-NISS): In addition to the correlated classical sequences (Xd, Yd), the agents Alice and Bob have access to a shared Bell state. They perform measurements on their respective parts of the entangled state and use the classical outputs along with (Xd, Yd) to simulate a target distribution QU,V.

Classical Common Randomness NISS (CR-NISS): In addition to the correlated classical sequences (Xd, Yd), the agents have access to a shared classical common random bit Z. They use (Z, Xd) and (Z, Yd) to simulate QU,V.

The key findings are:

For binary-output NISS scenarios, the set of feasible distributions for EA-NISS and CR-NISS are equal. Hence, there is no quantum advantage in these scenarios.

For non-binary output NISS scenarios, the set of distributions that can be simulated in the CR-NISS scenario has measure zero within the set of distributions simulatable in the EA-NISS scenario. This demonstrates quantum advantage in non-binary output NISS.

The proofs rely on Fourier analysis techniques and show that any distribution generated in the EA-NISS scenario can be simulated in the corresponding CR-NISS scenario for the binary output case, while the converse is not true for the non-binary case.

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Quantum Advantage in Non-Interactive Source Simulation

by Hojat Allah ... at arxiv.org 05-03-2024

https://arxiv.org/pdf/2402.00242.pdf

Deeper Inquiries

What are some practical applications where the demonstrated quantum advantage in non-binary output NISS scenarios could be leveraged

The demonstrated quantum advantage in non-binary output NISS scenarios could be leveraged in various practical applications where secure and efficient communication and computation are essential. One application could be in secure multi-party computation, where parties need to jointly compute a function without revealing their private inputs. The quantum advantage in NISS scenarios could enable more efficient and secure protocols for multi-party computation, ensuring privacy and integrity of the computation process. Additionally, in cryptographic parameter generation, the quantum advantage could lead to the generation of more secure and robust cryptographic keys and parameters, enhancing the overall security of cryptographic systems. Furthermore, in anonymous communication systems like blockchain networks, leveraging quantum advantage in NISS scenarios could enhance the anonymity and privacy of transactions and communications, ensuring a higher level of security and confidentiality.

Can the techniques developed in this work be extended to analyze quantum advantage in other information-theoretic tasks beyond NISS

The techniques developed in this work can be extended to analyze quantum advantage in other information-theoretic tasks beyond NISS. For example, the framework and analysis used to compare the feasibility of distributions in EA-NISS and CR-NISS scenarios can be applied to study quantum advantage in other communication protocols, cryptographic schemes, and quantum information processing tasks. By adapting the concepts of entanglement-assisted simulation and classical common randomness to different scenarios, researchers can explore the quantum advantage in various information-theoretic tasks such as quantum key distribution, quantum secure communication, quantum error correction, and quantum cryptography. This extension can provide insights into the potential benefits of quantum resources in improving the efficiency, security, and reliability of various information processing tasks.

How might the insights from this work inform the design of quantum protocols for secure multi-party computation and anonymous communication

The insights from this work can inform the design of quantum protocols for secure multi-party computation and anonymous communication by highlighting the advantages and limitations of using quantum resources in these scenarios. In secure multi-party computation, understanding the conditions under which quantum advantage can be achieved in NISS scenarios can guide the development of more efficient and secure quantum protocols for secure computation among multiple parties. By leveraging the quantum advantage demonstrated in non-binary output NISS scenarios, researchers can design quantum protocols that offer enhanced security, privacy, and efficiency in multi-party computation tasks. Similarly, in anonymous communication systems, the insights from this work can help in designing quantum-enhanced protocols that provide stronger anonymity guarantees and privacy protection for users in decentralized networks like blockchain. By incorporating quantum resources effectively, protocols for anonymous communication can achieve higher levels of security and confidentiality, ensuring the privacy of users' transactions and communications.