Related papers: New bounds on classical and quantum one-way commun…
We show that for a relation $f\subseteq \{0,1\}^n\times \mathcal{O}$ and a function $g:\{0,1\}^{m}\times \{0,1\}^{m} \rightarrow \{0,1\}$ (with $m= O(\log n)$), $$\mathrm{R}_{1/3}(f\circ g^n) = \Omega\left(\mathrm{R}_{1/3}(f) \cdot…
We study a new type of separation between quantum and classical communication complexity which is obtained using quantum protocols where all parties are efficient, in the sense that they can be implemented by small quantum circuits with…
Quantum mechanics allows operations to be in indefinite causal order. Recently there have been active discussions on enhanced communication strategies through exotic causal structures. In light of this, through the process matrix formalism,…
We study quantum communication protocols, in which the players' storage starts out in a state where one qubit is in a pure state, and all other qubits are totally mixed (i.e. in a random state), and no other storage is available (for…
Entanglement-assisted classical communication and transmission of a quantum system are the two quantum resources for information processing. Many information tasks can be performed using either quantum resource. However, this equivalence is…
Quantum resources can improve communication complexity problems (CCPs) beyond their classical constraints. One quantum approach is to share entanglement and create correlations violating a Bell inequality, which can then assist classical…
We study shared randomness in the context of multi-party number-in-hand communication protocols in the simultaneous message passing model. We show that with three or more players, shared randomness exhibits new interesting properties that…
The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan. At the end of the first section I examine tree-balancing. In the second section I summarize the…
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…
The class $FORMULA[s] \circ \mathcal{G}$ consists of Boolean functions computable by size-$s$ de Morgan formulas whose leaves are any Boolean functions from a class $\mathcal{G}$. We give lower bounds and (SAT, Learning, and PRG) algorithms…
In some scenarios there are ways of conveying information with many fewer, even exponentially fewer, qubits than possible classically. Moreover, some of these methods have a very simple structure--they involve only few message exchanges…
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 present new distributed quantum algorithms for fundamental distributed computing problems, namely, leader election, broadcast, Minimum Spanning Tree (MST), and Breadth-First Search (BFS) tree, in arbitrary networks. These algorithms are…
Representations of Boolean functions by real polynomials play an important role in complexity theory. Typically, one is interested in the least degree of a polynomial p(x_1,...,x_n) that approximates or sign-represents a given Boolean…
We introduce a framework for distributed quantum inference under communication constraints. In our model, $m$ distributed nodes each receive one copy of an unknown $d$-dimensional quantum state $\rho$, before communicating via a constrained…
Mutually orthogonal frequency squares (MOFS) of type $F(m\lambda;\lambda)$ generalize the structure of mutually orthogonal Latin squares: rather than each of $m$ symbols appearing exactly once in each row and in each column of each square,…
A two-party quantum communication process with classical inputs and outcomes can be simulated by replacing the quantum channel with a classical one. The minimal amount of classical communication required to reproduce the statistics of the…
We introduce a new quantum decoder based on a variant of the pretty good measurement, but defined via an alternative matrix quotient. We use this decoder to show new lower bounds on the error exponent both in the one-shot and asymptotic…
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…
In this work we focus our attention on distributed optimization problems in the context where the communication time between the server and the workers is non-negligible. We obtain novel methods supporting bidirectional compression (both…