Quantum Communication Advantage in TFNP

• URL: http://arxiv.org/abs/2411.03296v1
• Date: Tue, 05 Nov 2024 17:47:11 GMT
• Title: Quantum Communication Advantage in TFNP
• Authors: Mika Göös, Tom Gur, Siddhartha Jain, Jiawei Li,
• Abstract summary: We show a total search problem whose communication complexity in the quantum SMP (simultaneous message passing) model is exponentially smaller than in the classical two-way randomized model. We prove the classical lower bound using the structure-vs-randomness paradigm for analyzing communication protocols.
• Score: 8.777517901289341
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• Abstract: We exhibit a total search problem whose communication complexity in the quantum SMP (simultaneous message passing) model is exponentially smaller than in the classical two-way randomized model. Moreover, the quantum protocol is computationally efficient and its solutions are classically verifiable, that is, the problem lies in the communication analogue of the class TFNP. Our problem is a bipartite version of a query complexity problem recently introduced by Yamakawa and Zhandry (JACM 2024). We prove the classical lower bound using the structure-vs-randomness paradigm for analyzing communication protocols.

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