Related papers: On Arthur Merlin Games in Communication Complexity

This paper addresses the problem of generating a common random string with min-entropy k using an unlimited supply of noisy EPR pairs or quantum isotropic states, with minimal communication between Alice and Bob. The paper considers two…

In classical complexity theory, the two definitions of probabilistically checkable proofs -- the constraint satisfaction and the nonlocal games version -- are computationally equal in power. In the quantum setting, the situation is far less…

It is known that the mutual information, in the sense of Kolmogorov complexity, of any pair of strings x and y is equal to the length of the longest shared secret key that two parties can establish via a probabilistic protocol with…

Two parties observing correlated random variables seek to run an interactive communication protocol. How many bits must they exchange to simulate the protocol, namely to produce a view with a joint distribution within a fixed statistical…

We take an information theoretic perspective on a classical sparse-sampling noisy linear model and present an analytical expression for the mutual information, which plays central role in a variety of communications/processing problems.…

We introduce a simple model illustrating the role of context in communication and the challenge posed by uncertainty of knowledge of context. We consider a variant of distributional communication complexity where Alice gets some information…

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…

We present a protocol that transforms any quantum multi-prover interactive proof into a nonlocal game in which questions consist of logarithmic number of bits and answers of constant number of bits. As a corollary, this proves that the…

Using transfer-matrix method a correspondence between $2D$ classical spin systems ($2D$ Ising model and six-vertex model) and $1D$ quantum spin systems is considered. We find the transfer matrix in two limits - in a well-known…

We present a two-player communication task that can be solved by a protocol of polylogarithmic cost in the simultaneous message passing model with classical communication and shared entanglement, but requires exponentially more…

We introduce and study Certificate Game complexity, a measure of complexity based on the probability of winning a game where two players are given inputs with different function values and are asked to output some index $i$ such that…

Recently, Brassard et. al. conjectured that the fact that the maximal possible correlations between two non-local parties are the quantum-mechanical ones is linked to a reasonable restriction on communication complexity. We provide further…

We provide several advances to the understanding of the class of Quantum Merlin-Arthur proof systems (QMA), the quantum analogue of NP. Our central contribution is proving a longstanding conjecture that the Consistency of Local Density…

This paper introduces a novel lower bound on communication complexity using quantum relative entropy and mutual information, refining previous classical entropy-based results. By leveraging Uhlmann's lemma and quantum Pinsker inequalities,…

Computing set joins of two inputs is a common task in database theory. Recently, Van Gucht, Williams, Woodruff and Zhang [PODS 2015] considered the complexity of such problems in the natural model of (classical) two-party communication…

Romashchenko and Zimand~\cite{rom-zim:c:mutualinfo} have shown that if we partition the set of pairs $(x,y)$ of $n$-bit strings into combinatorial rectangles, then $I(x:y) \geq I(x:y \mid t(x,y)) - O(\log n)$, where $I$ denotes mutual…

The communication complexity of a quantum channel is the minimal amount of classical communication required for classically simulating a process of state preparation, transmission through the channel and subsequent measurement. It…

Multiple Tensor-Times-Matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower…

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 present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…