Related papers: The Partition Bound for Classical Communication Co…
In this work we introduce, both for classical communication complexity and query complexity, a modification of the 'partition bound' introduced by Jain and Klauck [2010]. We call it the 'public-coin partition bound'. We show that (the…
We investigate query-to-communication lifting theorems for models related to the quantum adversary bounds. Our results are as follows: 1. We show that the classical adversary bound lifts to a lower bound on randomized communication…
We present a linear program for the one-way version of the partition bound (denoted $\mathsf{prt}^1_\varepsilon(f)$). We show that it characterizes one-way randomized communication complexity $\mathsf{R}_\varepsilon^1(f)$ with shared…
Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient…
The quantum version of communication complexity allows the two communicating parties to exchange qubits and/or to make use of prior entanglement (shared EPR-pairs). Some lower bound techniques are available for qubit communication…
We show a nearly quadratic separation between deterministic communication complexity and the logarithm of the partition number, which is essentially optimal. This improves upon a recent power 1.5 separation of G\"o\"os, Pitassi, and Watson…
Quantum channel discrimination has been studied from an information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of unknown channel accesses. In this paper, we…
While exponential separations are known between quantum and randomized communication complexity for partial functions (Raz, STOC 1999), the best known separation between these measures for a total function is quadratic, witnessed by the…
In the last decade, various works have used statistics on relations to improve both the theory and practice of conjunctive query execution. Starting with the AGM bound which took advantage of relation sizes, later works incorporated…
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 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…
This document collects the lecture notes from my course "Communication Complexity (for Algorithm Designers),'' taught at Stanford in the winter quarter of 2015. The two primary goals of the course are: 1. Learn several canonical problems…
We study the query complexity analogue of the class TFNP of total search problems. We give a way to convert partial functions to total search problems under certain settings; we also give a way to convert search problems back into partial…
We prove upper bounds on deterministic communication complexity in terms of log of the rank and simple versions of the corruption bound. Our bounds are a simplified version of the results of Gavinsky and Lovett, using the same set of tools.…
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the…
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…
We define a quantum model for multiparty communication complexity and prove a simulation theorem between the classical and quantum models. As a result of our simulation, we show that if the quantum k-party communication complexity of a…
We show that almost all known lower bound methods for communication complexity are also lower bounds for the information complexity. In particular, we define a relaxed version of the partition bound of Jain and Klauck and prove that it…
Recently, there has been an increasing interest in designing distributed convex optimization algorithms under the setting where the data matrix is partitioned on features. Algorithms under this setting sometimes have many advantages over…
Consider the "Number in Hand" multiparty communication complexity model, where k players holding inputs x_1,...,x_k in {0,1}^n communicate to compute the value f(x_1,...,x_k) of a function f known to all of them. The main lower bound…