Related papers: A Direct Product Theorem for One-Way Quantum Commu…
Quantum entanglement cannot be used to achieve direct communication between remote parties, but it can reduce the communication needed for some problems. Let each of k parties hold some partial input data to some fixed k-variable function…
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…
We prove lower bounds for the direct sum problem for two-party bounded error randomised multiple-round communication protocols. Our proofs use the notion of information cost of a protocol, as defined by Chakrabarti, Shi, Wirth and Yao and…
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…
In this paper we provide new bounds on classical and quantum distributional communication complexity in the two-party, one-way model of communication. In the classical model, our bound extends the well known upper bound of Kremer, Nisan and…
A fundamental question in computer science is: Is it harder to solve $n$ instances independently than to solve them simultaneously? This question, known as the direct sum question or direct sum theorem, has been paid much attention in…
Sending quantum information reliably over long distances is a central challenge in quantum technology in general, and in quantum optics in particular, since most quantum communication relies on optical fibres or free-space links. Here, we…
Consider the following Simultaneous Message Passing (SMP) model for computing a relation f subset of X x Y x Z. In this model Alice, on input x in X and Bob, on input y in Y, send one message each to a third party Referee who then outputs a…
We study the effect that the amount of correlation in a bipartite distribution has on the communication complexity of a problem under that distribution. We introduce a new family of complexity measures that interpolates between the two…
We revisit the direct sum questions in communication complexity which asks whether the resource needed to solve $n$ communication problems together is (approximately) the sum of resources needed to solve these problems separately. Our work…
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,…
Bell's theorem implies that the outcomes of local measurements on two maximally entangled systems cannot be simulated without classical communication between the parties. The communication cost is finite for n Bell states, but it grows…
We analyze a task in which classical and quantum messages are simultaneously communicated via a noisy quantum channel, assisted with a limited amount of shared entanglement. We derive direct and converse bounds for the one-shot capacity…
Entangled quantum systems can exhibit correlations that cannot be simulated classically. For historical reasons such correlations are called "Bell inequality violations." We give two new two-player games with Bell inequality violations that…
We show a direct product result for two-way public coin communication complexity of all relations in terms of a new complexity measure that we define. Our new measure is a generalization to non-product distributions of the two-way product…
We study the relationship between various one-way communication complexity measures of a composed function with the analogous decision tree complexity of the outer function. We consider two gadgets: the AND function on 2 inputs, and the…
We present a new scheme for the compression of one-way quantum messages, in the setting of coherent entanglement assisted quantum communication. For this, we present a new technical tool that we call the convex split lemma, which is…
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…
Consider the expected query complexity of computing the $k$-fold direct product $f^{\otimes k}$ of a function $f$ to error $\varepsilon$ with respect to a distribution $\mu^k$. One strategy is to sequentially compute each of the $k$ copies…
Entanglement, a fundamental feature of quantum mechanics, has long been recognized as a valuable resource in enabling secure communications and surpassing classical limits. However, previous research has primarily concentrated on static…