Related papers: A note on the partition bound for one-way classica…
Communication complexity is a fundamental aspect of information science, concerned with the amount of communication required to solve a problem distributed among multiple parties. The standard quantification of one-way communication…
We provide the first capacity approaching coding schemes that robustly simulate any interactive protocol over an adversarial channel that corrupts any $\epsilon$ fraction of the transmitted symbols. Our coding schemes achieve a…
Let the randomized query complexity of a relation for error probability $\epsilon$ be denoted by $R_\epsilon(\cdot)$. We prove that for any relation $f \subseteq \{0,1\}^n \times \mathcal{R}$ and Boolean function $g:\{0,1\}^m \rightarrow…
We prove an $\Omega(n^{1-1/k} \log k \ /2^k)$ lower bound on the $k$-party number-in-hand communication complexity of collision-finding. This implies a $2^{n^{1-o(1)}}$ lower bound on the size of tree-like cutting-planes proofs of the bit…
We derive exact and asymptotic results for random partitions from general results in the semi-classical analysis of coherent states applied to the classical periodic Benjamin-Ono equation at critical regularity $s= -1/2$. We find classical…
We fully determine the communication complexity of approximating matrix rank, over any finite field $\mathbb{F}$. We study the most general version of this problem, where $0\leq r<R\leq n$ are given integers, Alice and Bob's inputs are…
In this paper, we present a new technique to obtain upper bounds on undirected unicast network information capacity. Using this technique, we characterize an upper bound, called partition bound, on the symmetric rate of information flow in…
We give improved separations for the query complexity analogue of the log-approximate-rank conjecture i.e. we show that there are a plethora of total Boolean functions on $n$ input bits, each of which has approximate Fourier sparsity at…
We prove a general lower bound on the bounded-error entanglement-assisted quantum communication complexity of Boolean functions. The bound is based on the concept that any classical or quantum protocol to evaluate a function on distributed…
The communication complexity of many fundamental problems reduces greatly when the communicating parties share randomness that is independent of the inputs to the communication task. Natural communication processes (say between humans)…
An open problem in communication complexity proposed by several authors is to prove that for every Boolean function f, the task of computing f(x AND y) has polynomially related classical and quantum bounded-error complexities. We solve a…
It has long been known that the existence of certain superquantum nonlocal correlations would cause communication complexity to collapse. The absurdity of a world in which any nonlocal binary function could be evaluated with a constant…
Quantum mechanics allows operations to be in indefinite causal order. Recently there have been active discussions on enhanced communication strategies through exotic causal structures. In light of this, through the process matrix formalism,…
We develop a novel and powerful technique for communication lower bounds, the pattern matrix method. Specifically, fix an arbitrary function f:{0,1}^n->{0,1} and let A_f be the matrix whose columns are each an application of f to some…
The set of all error--correcting block codes over a fixed alphabet with $q$ letters determines a recursively enumerable set of rational points in the unit square with coordinates $(R,\delta)$:= (relative transmission rate, relative minimal…
A two-party quantum communication process with classical inputs and outcomes can be simulated by replacing the quantum channel with a classical one. The minimal amount of classical communication required to reproduce the statistics of the…
In the coordinator model of communication with $s$ servers, given an arbitrary non-negative function $f$, we study the problem of approximating the sum $\sum_{i \in [n]}f(x_i)$ up to a $1 \pm \varepsilon$ factor. Here the vector $x \in R^n$…
When two agents of different computational capacities interact with the same environment, they need not compress a common semantic alphabet differently; they can induce different semantic alphabets altogether. We show that the quotient…
We consider the LOCAL model of distributed computing, where in a single round of communication each node can send to each of its neighbors a message of an arbitrary size. It is know that, classically, the round complexity of 3-coloring an…
The goal of demonstrating a quantum advantage with currently available experimental systems is of utmost importance in quantum information science. While this remains elusive for quantum computation, the field of communication complexity…