Related papers: Quantum Query-to-Communication Simulation Needs a …
A basic goal in complexity theory is to understand the communication complexity of number-on-the-forehead problems $f\colon(\{0,1\}^n)^{k}\to\{0,1\}$ with $k\gg\log n$ parties. We study the problems of inner product and set disjointness and…
We investigate the fundamental limit of quantum-secure covert communication over the lossy thermal noise bosonic channel, the quantum-mechanical model underlying many practical channels. We assume that the adversary has unlimited quantum…
Recent work has extended Bell's theorem by quantifying the amount of communication required to simulate entangled quantum systems with classical information. The general scenario is that a bipartite measurement is given from a set of…
In this paper we consider an application of the recently proposed quantum hashing technique for computing Boolean functions in the quantum communication model. The combination of binary functions on non-binary quantum hash function is done…
We study the $\textit{average-case deterministic query complexity}$ of boolean functions under a $\textit{uniform input distribution}$, denoted by $\mathrm{D}_\mathrm{ave}(f)$, the minimum average depth of zero-error decision trees that…
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…
We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathfrak{C}$ be a class of polynomial-size concepts, and suppose that $\mathfrak{C}$ can be PAC-learned with…
In this paper, we introduce the hybrid query complexity, denoted as $\mathrm{Q}(f;q)$, which is the minimal query number needed to compute $f$, when a classical decision tree is allowed to call $q'$-query quantum subroutines for any $q'\leq…
We prove a direct sum theorem for bounded round entanglement-assisted quantum communication complexity. To do so, we use the fully quantum definition for information cost and complexity that we recently introduced, and use both the fact…
The problem of learning Boolean linear functions from quantum examples w.r.t. the uniform distribution can be solved on a quantum computer using the Bernstein-Vazirani algorithm. A similar strategy can be applied in the case of noisy…
Let $f : \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}$ be a 2-party function. For every product distribution $\mu$ on $\{0,1\}^n \times \{0,1\}^n$, we show that $$\mathsf{CC}^\mu_{0.49}(f) = O\left(\left(\log \mathsf{prt}_{1/8}(f) \cdot…
The CONGEST and CONGEST-CLIQUE models have been carefully studied to represent situations where the communication bandwidth between processors in a network is severely limited. Messages of only $O(log(n))$ bits of information each may be…
We prove a lower bound on the communication complexity of computing the $n$-fold xor of an arbitrary function $f$, in terms of the communication complexity and rank of $f$. We prove that $D(f^{\oplus n}) \geq n \cdot…
We consider several models of 1-round classical and quantum communication, some of these models have not been defined before. We "almost separate" the models of simultaneous quantum message passing with shared entanglement and the model of…
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…
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…
Recent breakthroughs in quantum query complexity have shown that any formula of size n can be evaluated with O(sqrt(n)log(n)/log log(n)) many quantum queries in the bounded-error setting [FGG08, ACRSZ07, RS08b, Rei09]. In particular, this…
We give the first exponential separation between quantum and classical multi-party communication complexity in the (non-interactive) one-way and simultaneous message passing settings. For every k, we demonstrate a relational communication…
We develop and apply an extension of the randomized compiling (RC) protocol that includes a special treatment of neighboring qubits and dramatically reduces crosstalk effects caused by the application of faulty gates on superconducting…
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…