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This research establishes a significant separation between classical and quantum communication complexity, proving that certain randomized tasks require exponentially more resources classically than with just two quantum messages. By refining theoretical frameworks to show polylogarithmic quantum advantages against exponential classical lower bounds, the study advances our understanding of fundamental limits in information exchange. These findings are critical for developing efficient quantum networks and verifying the intrinsic superiority of quantum protocols in multi-party computation scenarios.
Quantum Communication Surpasses Classical Limits with Root-N Advantage
Could a computational task require exponentially more randomised communication than its quantum counterpart? New work demonstrates polylogarithmic quantum communication against an eΩ(√n) lower bound for randomised communication using just two messages, a marked improvement over the previous separation of eΩ(n^(1/6)). Further results extend this to scenarios employing constant numbers of quantum messages where randomised complexity scales as Ω(n¹−ε) for any fixed ε > 0.
A randomised communication lower bound of eΩ(√n) now exists for total functions utilising two quantum messages; previously, Gavinsky's framework demonstrated only eΩ(n1/6). This improvement builds upon existing work in quantum communication complexity which seeks to understand how much more efficiently tasks can be completed using quantum systems compared with classical methods. The research also extended this result, achieving similar separations with constant numbers of quantum messages where randomised communication scales as Ω(n1−ε), for any…
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