Related papers: A direct sum theorem in communication complexity v…
We present efficient and practical algorithms for a large, distributed system of processors to achieve reliable computations in a secure manner. Specifically, we address the problem of computing a general function of several private inputs…
We give a direct product theorem for the entanglement-assisted interactive quantum communication complexity of an $l$-player predicate $\mathsf{V}$. In particular we show that for a distribution $p$ that is product across the input sets of…
We consider implementations of a bipartite unitary on many pairs of unknown input states by local operation and classical communication assisted by shared entanglement. We investigate to what extent the entanglement cost and the classical…
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…
Let f subset of X x Y x Z be a relation. Let the public coin one-way communication complexity of f, with worst case error 1/3, be denoted R^{1,pub}_{1/3}(f). We show that if for computing f^k (k independent copies of f), o(k…
We consider the task of compression of information when the source of the information and the destination do not agree on the prior, i.e., the distribution from which the information is being generated. This setting was considered…
We study the communication complexity of symmetric XOR functions, namely functions $f: \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}$ that can be formulated as $f(x,y)=D(|x\oplus y|)$ for some predicate $D: \{0,1,...,n\} \rightarrow…
The main result of this paper is an optimal strong direct product result for the two-party public-coin randomized communication complexity of the Tribes function. This is proved by providing an alternate proof of the optimal lower bound of…
A central question in classical information theory is that of source compression, which is the task where Alice receives a sample from a known probability distribution and needs to transmit it to the receiver Bob with small error. This…
State redistribution is the protocol in which, given an arbitrary tripartite quantum state, with two of the subsystems initially being with Alice and one being with Bob, the goal is for Alice to send one of her subsystems to Bob, possibly…
We study the direct-sum problem for $k$-party ``Number On the Forehead'' (NOF) deterministic communication complexity. We prove several positive results, showing that the complexity of computing a function $f$ in this model, on $\ell$…
Communication compression is a common technique in distributed optimization that can alleviate communication overhead by transmitting compressed gradients and model parameters. However, compression can introduce information distortion,…
We consider the problem of the classical simulation of quantum measurements in the scenario of communication complexity. Regev and Toner (2007) have presented a 2-bit protocol which simulates one particular correlation function arising from…
This paper considers distributed nonconvex optimization with the cost functions being distributed over agents. Noting that information compression is a key tool to reduce the heavy communication load for distributed algorithms as agents…
The focus of this paper is on {\em quantum distributed} computation, where we investigate whether quantum communication can help in {\em speeding up} distributed network algorithms. Our main result is that for certain fundamental network…
Modern applied optimization problems become more and more complex every day. Due to this fact, distributed algorithms that can speed up the process of solving an optimization problem through parallelization are of great importance. The main…
A Direct Sum Theorem holds in a model of computation, when solving some k input instances together is k times as expensive as solving one. We show that Direct Sum Theorems hold in the models of deterministic and randomized decision trees…
We prove a direct product theorem for the one-way entanglement-assisted quantum communication complexity of a general relation $f\subseteq\mathcal{X}\times\mathcal{Y}\times\mathcal{Z}$. For any $\varepsilon, \zeta > 0$ and any $k\geq1$, we…
Coded source compression, also known as source compression with helpers, has been a major variant of distributed source compression, but has hitherto received little attention in the quantum regime. This work treats and solves the…
Information theoretically secure multi-party computation (MPC) is a central primitive of modern cryptography. However, relatively little is known about the communication complexity of this primitive. In this work, we develop powerful…