New lower bounds for CDS and $f$-routing
New lower bounds tie robust CDS randomness to communication complexity and inner-product routing entanglement to sign rank.
The paper studies entanglement and randomness costs related to non-local quantum computation, focusing on f-routing and robust conditional disclosure of secrets. It proves that robust CDS shared-randomness cost is at least the logarithm of deterministic simultaneous-message-passing communication complexity, even with unlimited communication and private randomness, and that the bound is tight for equality. For one-sided-perfect f-routing, a sign-rank argument gives a linear entanglement lower bound for the inner-product function in both one-sided settings, matching the known upper bound.
- Robust CDS shared-randomness cost is at least log of deterministic SMP complexity.
- The CDS lower bound is tight for the equality function.
- One-sided-perfect inner-product routing needs linear entanglement, matching the upper bound.
From the original article
1 min read at arxiv.orgUnderstanding the entanglement cost of non-local quantum computation (NLQC) is relevant to complexity theory, cryptography, quantum gravity, and related areas. A central special case is $f$-routing, motivated in part by quantum position verification. Proving lower bounds on its entanglement cost in the fully robust setting has been a major open problem in NLQC.
By Atsuya Hasegawa · arxiv.org
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