Related papers: Communication Complexity of Collision
As a consequence of Bell's theorem, the statistics of measurements on some entangled states cannot be simulated with local hidden variables alone. The amount of communication that must be supplied is an intuitive quantifier of…
The *algebrization barrier*, proposed by Aaronson and Wigderson (STOC '08, ToCT '09), captures the limitations of many complexity-theoretic techniques based on arithmetization. Notably, several circuit lower bounds that overcome 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…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
We consider a Bayesian persuasion problem where the persuader and the decision maker communicate through an imperfect channel that has a fixed and limited number of messages and is subject to exogenous noise. We provide an upper bound on…
In distributed systems, situations often arise where some nodes each holds a collection of tokens, and all nodes collectively need to determine whether all tokens are distinct. For example, if each token represents a logged-in user, the…
We introduce a new theoretical framework for deriving lower bounds on data movement in bilinear algorithms. Bilinear algorithms are a general representation of fast algorithms for bilinear functions, which include computation of matrix…
In this note, we give a quantum algorithm that finds collisions in arbitrary r-to-one functions after only O((N/r)^(1/3)) expected evaluations of the function. Assuming the function is given by a black box, this is more efficient than the…
We propose a communication protocol exploiting correlations between two events with a definite time-ordering: a) the outcome of a {\em weak measurement} on a spin, and b) the outcome of a subsequent ordinary measurement on the spin. In our…
In this paper, we provide a simple framework for deriving one-shot achievable bounds for some problems in quantum information theory. Our framework is based on the joint convexity of the exponential of the collision relative entropy, and is…
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…
We prove a tight quantum query lower bound $\Omega(n^{k/(k+1)})$ for the problem of deciding whether there exist $k$ numbers among $n$ that sum up to a prescribed number, provided that the alphabet size is sufficiently large. This is an…
We show a tight lower bound of $\Omega(N \log\log N)$ on the number of transmissions required to compute the parity of $N$ input bits with constant error in a noisy communication network of $N$ randomly placed sensors, each having one input…
Bell inequalities limit the possible observations of non-communicating parties. Here, we present analogous inequalities for any number of communicating parties under the causal constraints of static causal order, definite causal order, and…
Building on previous results of Xing, we give new lower bounds on the rate of intersecting codes over large alphabets. The proof is constructive, and uses algebraic geometry, although nothing beyond the basic theory of linear systems on…
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…
Suppose that a transmitter Alice potentially wishes to communicate with a receiver Bob over an adversarially jammed binary channel. An active adversary James eavesdrops on their communication over a binary symmetric channel (BSC(q)), and…
This paper applies Information Theoretic analysis to packet-based random multiple access communication systems. A new channel coding approach is proposed for coding within each data packet with built-in support for bursty traffic…
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…
To reproduce in a local hidden variables theory correlations that violate Bell inequalities, communication must occur between the parties. We show that the amount of violation of a Bell inequality imposes a lower bound on the average…