Related papers: On the communication complexity of XOR functions
We study an extension of the standard two-party communication model in which Alice and Bob hold probability distributions $p$ and $q$ over domains $X$ and $Y$, respectively. Their goal is to estimate \[ \mathbb{E}_{x \sim p,\, y \sim…
One of the best lower bound methods for the quantum communication complexity of a function H (with or without shared entanglement) is the logarithm of the approximate rank of the communication matrix of H. This measure is essentially…
I show that a simple multi-party communication task can be performed more efficiently with quantum communication than with classical communication, even with low detection efficiency $\eta$. The task is a communication complexity problem in…
We characterize the approximate monomial complexity, sign monomial complexity , and the approximate L 1 norm of symmetric functions in terms of simple combinatorial measures of the functions. Our characterization of the approximate L 1 norm…
Non-local games are widely studied as a model to investigate the properties of quantum mechanics as opposed to classical mechanics. In this paper, we consider a subset of non-local games: symmetric XOR games of $n$ players with 0-1 valued…
Let $f$ denote length preserving function on words. A classical algorithm can be considered as $T$ iterated applications of black box representing $f$, beginning with input word $x$ of length $n$. It is proved that if $T=O(2^{n/(7+e)}), e…
We introduce a restriction of the classical 2-party deterministic communication protocol where Alice and Bob are restricted to using only comparison functions. We show that the complexity of a function in the model is, up to a constant…
Buhrman, Cleve and Wigderson (STOC'98) observed that for every Boolean function $f : \{-1, 1\}^n \to \{-1, 1\}$ and $\bullet : \{-1, 1\}^2 \to \{-1, 1\}$ the two-party bounded-error quantum communication complexity of $(f \circ \bullet)$ is…
We show that for a relation $f\subseteq \{0,1\}^n\times \mathcal{O}$ and a function $g:\{0,1\}^{m}\times \{0,1\}^{m} \rightarrow \{0,1\}$ (with $m= O(\log n)$), $$\mathrm{R}_{1/3}(f\circ g^n) = \Omega\left(\mathrm{R}_{1/3}(f) \cdot…
We present and experimentally demonstrate a communication protocol that employs shared entanglement to reduce errors when sending a bit over a particular noisy classical channel. Specifically, it is shown that, given a single use of this…
There are few explicit examples of two player nonlocal games with a large gap between classical and quantum value. One of the reasons is that estimating the classical value is usually a hard computational task. This paper is devoted to…
Equality and disjointness are two of the most studied problems in communication complexity. They have been studied for both classical and also quantum communication and for various models and modes of communication. Buhrman et al. [Buh98]…
Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…
Computational models typically assume that operations are applied in a fixed sequential order. In recent years several works have looked at relaxing this assumption, considering computations without any fixed causal structure and showing…
We investigate the randomized and quantum communication complexities of the well-studied Equality function with small error probability $\epsilon$, getting optimal constant factors in the leading terms in a number of different models. In…
We establish the classical capacity of optical quantum channels as a sharp transition between two regimes---one which is an error-free regime for communication rates below the capacity, and the other in which the probability of correctly…
We study the problem of simulating protocols in a quantum communication setting over noisy channels. This problem falls at the intersection of quantum information theory and quantum communication complexity, and it will be of importance for…
Here we revisit the quantum algorithms for obtaining Forrelation [Aaronson et al, 2015] values to evaluate some of the well-known cryptographically significant spectra of Boolean functions, namely the Walsh spectrum, the cross-correlation…
One of the most intriguing facts about communication using quantum states is that these states cannot be used to transmit more classical bits than the number of qubits used, yet there are ways of conveying information with exponentially…
How could quantum cryptography help us achieve what are not achievable in classical cryptography? In this work we study the classical cryptographic problem that two parties would like to perform secure computations with long outputs. As a…