Related papers: Quantum Query-to-Communication Simulation Needs a …

We determine the quantum query complexity of oracle identification on the hyperoctahedral group $B_N = \{\pm 1\}^N \rtimes S_N$ with respect to the natural representation: $Q_{LV}(B_N) = 2(N-1)$ for all $N \ge 2$. This is twice the…

Sensitivity conjecture is a longstanding and fundamental open problem in the area of complexity measures of Boolean functions and decision tree complexity. The conjecture postulates that the maximum sensitivity of a Boolean function is…

We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…

We study the problem of simulating protocols in a quantum communication setting over noisy channels. This problem falls at the intersection of quantum information theory and quantum communication complexity, and it will be of importance for…

We consider a variation of the multi-party communication complexity scenario where the parties are supplied with an extra resource: particles in an entangled quantum state. We show that, although a prior quantum entanglement cannot be used…

We show that any quantum algorithm deciding whether an input function $f$ from $[n]$ to $[n]$ is 2-to-1 or almost 2-to-1 requires $\Theta(n)$ queries to $f$. The same lower bound holds for determining whether or not a function $f$ from…

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…

An XOR function is a function of the form g(x,y) = f(x + y), for some boolean function f on n bits. We study the quantum and classical communication complexity of XOR functions. In the case of exact protocols, we completely characterise…

Let $\R(\cdot)$ stand for the bounded-error randomized query complexity. We show that for any relation $f \subseteq \{0,1\}^n \times \mathcal{S}$ and partial Boolean function $g \subseteq \{0,1\}^n \times \{0,1\}$, $\R_{1/3}(f \circ g^n) =…

In this paper, we show a direct product theorm in the model of two-party bounded-round public-coin randomized communication complexity. For a relation f subset of X times Y times Z (X,Y,Z are finite sets), let R^{(t), pub}_e (f) denote the…

We show a partial Boolean function $f$ together with an input $x\in f^{-1}\left(*\right)$ such that both $C_{\bar{0}}\left(f,x\right)$ and $C_{\bar{1}}\left(f,x\right)$ are at least $C\left(f\right)^{2-o\left(1\right)}$. Due to recent…

Let $f: \{0,1\}^n \to \{0, 1\}$ be a boolean function, and let $f_\land (x, y) = f(x \land y)$ denote the AND-function of $f$, where $x \land y$ denotes bit-wise AND. We study the deterministic communication complexity of $f_\land$ and show…

In this work we introduce an intermediate setting between quantum nonlocality and communication complexity problems. More precisely, we study the value of XOR games $G$ when Alice and Bob are allowed to use a limited amount of one-way…

In this paper the Neciporuk method for proving lower bounds on the size of Boolean formulae is reformulated in terms of one-way communication complexity. We investigate the scenarios of probabilistic formulae, nondeterministic formulae, and…

We demonstrate a two-player communication problem that can be solved in the one-way quantum model by a 0-error protocol of cost O (log n) but requires exponentially more communication in the classical interactive (bounded error) model.

$\newcommand{\F}{\mathbb{F}}$We study the Boolean function parameters sensitivity ($s$), block sensitivity ($bs$), and alternation ($alt$) under specially designed affine transforms. For a function $f:\F_2^n\to \{0,1\}$, and $A=Mx+b$ for $M…

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…

We first give an $\O(2^{n/3})$ quantum algorithm for the 0-1 Knapsack problem with $n$ variables. More generally, for 0-1 Integer Linear Programs with $n$ variables and $d$ inequalities we give an $\O(2^{n/3}n^d)$ quantum algorithm. For $d…

For any Boolean function $f:\{0,1\}^n \to \{0,1\}$ with a complexity measure having value $k \ll n$, is it possible to restrict the function $f$ to $\Theta(k)$ variables while keeping the complexity preserved at $\Theta(k)$? This question,…

$\newcommand{\EC}{\mathsf{EC}}\newcommand{\KW}{\mathsf{KW}}\newcommand{\DT}{\mathsf{DT}}\newcommand{\psens}{\mathsf{psens}} \newcommand{\calB}{{\cal B}} $ For a Boolean function $f:\{0,1\}^n \to \{0,1\}$ computed by a circuit $C$ over a…