Noise Thresholds for Amplification: Quantum Foundations From Classical Fault-Tolerant Computation
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It has long been known that certain superquantum nonlocal correlations collapse communication complexity, and it is conjectured that a statement like "communication complexity is not trivial" may provide an intuitive information-theoretic axiom for quantum mechanics. With the goal of addressing this conjecture, we take aim at collapsing communication complexity using weaker nonlocal correlations, and present a no-go theorem for a broad class of approaches. To achieve this, we investigate fault-tolerant computation by noisy circuits in a new light. Our main technical result is that, perhaps surprisingly, noiseless XOR gates are not more helpful than noisy ones in read-once formulas that have noisy AND gates for the task of building amplifiers. We also formalize a connection between fault-tolerant computation and amplification, and highlight new directions and open questions in fault-tolerant computation with noisy circuits. Our results inform the relationship between superquantum nonlocality and the collapse of communication complexity.
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