相关论文: Lower bounds for quantum communication complexity

Communication complexity, which quantifies the minimum communication required for distributed computation, offers a natural setting for investigating the capabilities and limitations of quantum mechanics in information processing. We…

We consider the problem of testing whether a Boolean function has Fourier degree $\leq k$ or it is $\epsilon$-far from any Boolean function with Fourier degree $\leq k$. We improve the known lower bound of $\Omega(k)$ \cite{BBM11,CGM10}, to…

In this article we establish new bounds on the quantum communication complexity of distributed problems. Specifically, we consider the amount of communication that is required to transform a bipartite state into another, typically more…

We prove new bounds on the quantum communication complexity of the disjointness and equality problems. For the case of exact and non-deterministic protocols we show that these complexities are all equal to n+1, the previous best lower bound…

We establish novel connections between magic in quantum circuits and communication complexity. In particular, we show that functions computable with low magic have low communication cost. Our first result shows that the $\mathsf{D}\|$…

In this paper, we focus on the quantum communication complexity of functions of the form $f \circ G = f(G(X_1, Y_1), \ldots, G(X_n, Y_n))$ where $f: \{0, 1\}^n \to \{0, 1\}$ is a symmetric function, $G: \{0, 1\}^j \times \{0, 1\}^k \to \{0,…

We present a simple and general simulation technique that transforms any black-box quantum algorithm (a la Grover's database search algorithm) to a quantum communication protocol for a related problem, in a way that fully exploits the…

The level-$k$ $\ell_1$-Fourier weight of a Boolean function refers to the sum of absolute values of its level-$k$ Fourier coefficients. Fourier growth refers to the growth of these weights as $k$ grows. It has been extensively studied for…

The process of state preparation, its transmission and subsequent measurement can be classically simulated through the communication of some amount of classical information. Recently, we proved that the minimal communication cost is the…

Buhrman, Cleve and Wigderson (STOC'98) showed that for every Boolean function f : {-1,1}^n to {-1,1} and G in {AND_2, XOR_2}, the bounded-error quantum communication complexity of the composed function f o G equals O(Q(f) log n), where Q(f)…

We exhibit a Boolean function for which the quantum communication complexity is exponentially larger than the classical information complexity. An exponential separation in the other direction was already known from the work of Kerenidis…

Communication complexity is the amount of communication needed to compute a function when the function inputs are distributed over multiple parties. In its simplest form, one-way communication complexity, Alice and Bob compute a function…

We give lower bounds on the communication complexity required to solve several computational problems in a distributed-memory parallel machine, namely standard matrix multiplication, stencil computations, comparison sorting, and the Fast…

We consider the class of functions whose value depends only on the intersection of the input X_1,X_2, ..., X_t; that is, for each F in this class there is an f_F: 2^{[n]} \to {0,1}, such that F(X_1,X_2, ..., X_t) = f_F(X_1 \cap X_2 \cap ...…

One of the strongest techniques available for showing lower bounds on quantum communication complexity is the logarithm of the approximation rank of the communication matrix--the minimum rank of a matrix which is entrywise close to the…

We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions…

We study an extension of the standard two-party communication model in which Alice and Bob hold probability distributions $p$ and $q$ over domains $X$ and $Y$, respectively. Their goal is to estimate \[ \mathbb{E}_{x \sim p,\, y \sim…

We study space-bounded communication complexity for unitary implementation in distributed quantum processors, where we restrict the number of qubits per processor to ensure practical relevance and technical non-triviality. We model…

We study the question of how much classical communication is needed when Alice is given a classical description of a quantum state $|\psi\rangle$ for Bob to recover any expectation value $\langle \psi | M |\psi\rangle$ given an observable…

For any function $f: X \times Y \to Z$, we prove that $Q^{*\text{cc}}(f) \cdot Q^{\text{OIP}}(f) \cdot (\log Q^{\text{OIP}}(f) + \log |Z|) \geq \Omega(\log |X|)$. Here, $Q^{*\text{cc}}(f)$ denotes the bounded-error communication complexity…