Related papers: Lower bounds on the communication complexity of tw…
We prove an optimal $\Omega(n)$ lower bound on the randomized communication complexity of the much-studied Gap-Hamming-Distance problem. As a consequence, we obtain essentially optimal multi-pass space lower bounds in the data stream model…
We consider the task of minimizing the sum of convex functions stored in a decentralized manner across the nodes of a communication network. This problem is relatively well-studied in the scenario when the objective functions are smooth, or…
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…
We introduce new models and new information theoretic measures for the study of communication complexity in the natural peer-to-peer, multi-party, number-in-hand setting. We prove a number of properties of our new models and measures, and…
In this thesis, we are interested in the limits of quantum communication with and without entanglement, and with and without noise assumptions on the communication setup. When a sender and a receiver are connected by a communication line…
We study randomized and quantum efficiency lower bounds in communication complexity. These arise from the study of zero-communication protocols in which players are allowed to abort. Our scenario is inspired by the physics setup of Bell…
Information theory establishes the ultimate limits on performance for noisy communication systems [Shannon48]. An accurate model of a physical communication device must include quantum effects, but typically including these makes the theory…
We prove lower bounds for the direct sum problem for two-party bounded error randomised multiple-round communication protocols. Our proofs use the notion of information cost of a protocol, as defined by Chakrabarti, Shi, Wirth and Yao and…
A major open problem in communication complexity is whether or not quantum protocols can be exponentially more efficient than classical protocols on _total_ Boolean functions in the two-party interactive model. The answer appears to be…
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…
Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is to minimize a quadratic cost function in the state variables and…
We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower…
This work addresses two problems in the context of two-party communication complexity of functions. First, it concludes the line of research, which can be viewed as demonstrating qualitative advantage of quantum communication in the three…
One of the strongest techniques available for showing lower bounds on quantum communication complexity is the logarithm of the approximation rank of the communication matrix--the minimum rank of a matrix which is entrywise close to the…
Symmetric quantum signal processing provides a parameterized representation of a real polynomial, which can be translated into an efficient quantum circuit for performing a wide range of computational tasks on quantum computers. For a given…
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…
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 give lower bounds on the communication complexity required to solve several computational problems in a distributed-memory parallel machine, namely standard matrix multiplication, stencil computations, comparison sorting, and the Fast…
We describe new lower bounds for randomized communication complexity and query complexity which we call the partition bounds. They are expressed as the optimum value of linear programs. For communication complexity we show that the…
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…