Related papers: A direct sum theorem in communication complexity v…
We define a new notion of information cost for quantum protocols, and a corresponding notion of quantum information complexity for bipartite quantum channels, and then investigate the properties of such quantities. These are the fully…
In this paper, we prove a strong XOR lemma for bounded-round two-player randomized communication. For a function $f:\mathcal{X}\times \mathcal{Y}\rightarrow\{0,1\}$, the $n$-fold XOR function $f^{\oplus n}:\mathcal{X}^n\times…
Three decades of research in communication complexity have led to the invention of a number of techniques to lower bound randomized communication complexity. The majority of these techniques involve properties of large submatrices…
In this paper we explore fundamental problems in randomized communication complexity such as computing Set Intersection on sets of size $k$ and Equality Testing between vectors of length $k$. Sa\u{g}lam and Tardos and Brody et al. showed…
Direct sum theorems state that the cost of solving $k$ instances of a problem is at least $\Omega(k)$ times the cost of solving a single instance. We prove the first such results in the randomised parity decision tree model. We show that a…
Shared entanglement is a resource available to parties communicating over a quantum channel, much akin to public coins in classical communication protocols. Whereas shared randomness does not help in the transmission of information, or…
We prove the existence of (one-way) communication tasks with a subconstant versus superconstant asymptotic gap, which we call "doubly infinite," between their quantum information and communication complexities. We do so by studying the…
We consider parameter estimation in distributed networks, where each sensor in the network observes an independent sample from an underlying distribution and has $k$ bits to communicate its sample to a centralized processor which computes…
We consider the problem of estimating the arithmetic average of a finite collection of real vectors stored in a distributed fashion across several compute nodes subject to a communication budget constraint. Our analysis does not rely on any…
In order to mitigate the high communication cost in distributed and federated learning, various vector compression schemes, such as quantization, sparsification and dithering, have become very popular. In designing a compression method, one…
The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan. At the end of the first section I examine tree-balancing. In the second section I summarize the…
We study shared randomness in the context of multi-party number-in-hand communication protocols in the simultaneous message passing model. We show that with three or more players, shared randomness exhibits new interesting properties that…
This paper studies the distributed linearly separable computation problem, which is a generalization of many existing distributed computing problems such as distributed gradient descent and distributed linear transform. In this problem, a…
We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $\sum_{i = 1}^N f_i (x)$. This problem arises naturally in…
A strong direct product theorem (SDPT) states that solving n instances of a problem requires Omega(n) times the resources for a single instance, even to achieve success probability exp(-Omega(n)). We prove that quantum communication…
Every known communication problem whose randomized communication cost is constant (independent of the input size) can be reduced to $k$-Hamming Distance, that is, solved with a constant number of deterministic queries to some $k$-Hamming…
There is a close relationship between the communication complexity and information complexity of communication problems, as demonstrated by results such as Shannon's noiseless source coding theorem, and the Slepian-Wolf theorem. Here, we…
Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
We analyse the problem of transmitting a number of unknown quantum states or one composite system in one go. We derive a lower bound on the performance of such process, measured in the entanglement fidelity. The obtained bound is…
Given a correlation generated by a (possibly quantum) communication network, we study the amount of shared randomness required to generate it. We develop a novel upper bound for approximating distributions generated by arbitrary networks…