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Electronic Colloquium on Computational Complexity

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Reports tagged with Quantum Communication:
TR07-058 | 9th June 2007
Dmitry Gavinsky

Classical Interaction Cannot Replace a Quantum Message

Revisions: 1

We demonstrate a two-player communication problem that can be solved in the one-way quantum model by a 0-error protocol of cost O(log n) but requires exponentially more communication in the classical interactive (two-way) model.

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TR07-074 | 7th August 2007
Dmitry Gavinsky, Pavel Pudlak

Exponential Separation of Quantum and Classical Non-Interactive Multi-Party Communication Complexity

We give the first exponential separation between quantum and
classical multi-party
communication complexity in the (non-interactive) one-way and
simultaneous message
passing settings.
For every k, we demonstrate a relational communication problem
between k parties
that can be solved exactly by a quantum simultaneous message passing
protocol of
cost ... more >>>

TR08-109 | 10th November 2008
Marc Kaplan, Sophie Laplante

Kolmogorov complexity and combinatorial methods in communication complexity

A very important problem in quantum communication complexity is to show that there is, or isn?t, an exponential gap between randomized and quantum complexity for a total function. There are currently no clear candidate functions for such a separation; and there are fewer and fewer randomized lower bound techniques that ... more >>>

TR19-006 | 17th January 2019
Anna Gal, Ridwan Syed

Upper Bounds on Communication in terms of Approximate Rank

Revisions: 1

We show that any Boolean function with approximate rank $r$ can be computed by bounded error quantum protocols without prior entanglement of complexity $O( \sqrt{r} \log r)$. In addition, we show that any Boolean function with approximate rank $r$ and discrepancy $\delta$ can be computed by deterministic protocols of complexity ... more >>>

TR20-101 | 7th July 2020
Uma Girish, Ran Raz, Wei Zhan

Lower Bounds for XOR of Forrelations

The Forrelation problem, first introduced by Aaronson [AA10] and Aaronson and Ambainis [AA15], is a well studied computational problem in the context of separating quantum and classical computational models. Variants of this problem were used to give tight separations between quantum and classical query complexity [AA15]; the first separation between ... more >>>

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