Related papers: Direct Sum Theorem for Bounded Round Quantum Commu…
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…
We define a new notion of information cost for quantum protocols, and a corresponding notion of quantum information complexity for bipartite quantum channels, and then investigate the properties of such quantities. These are the fully…
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 prove a general lower bound on the bounded-error entanglement-assisted quantum communication complexity of Boolean functions. The bound is based on the concept that any classical or quantum protocol to evaluate a function on distributed…
We show optimal Direct Sum result for the one-way entanglement-assisted quantum communication complexity for any relation f subset of X x Y x Z. We show: Q^{1,pub}(f^m) = Omega(m Q^{1,pub}(f)), where Q^{1,pub}(f), represents the one-way…
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…
We show a near optimal direct-sum theorem for the two-party randomized communication complexity. Let $f\subseteq X \times Y\times Z$ be a relation, $\varepsilon> 0$ and $k$ be an integer. We show,…
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…
We prove a direct product theorem for the one-way entanglement-assisted quantum communication complexity of a general relation $f\subseteq\mathcal{X}\times\mathcal{Y}\times\mathcal{Z}$. For any $\varepsilon, \zeta > 0$ and any $k\geq1$, we…
We revisit the quantum reverse Shannon theorem, a central result in quantum information theory that characterizes the resources needed to simulate quantum channels when entanglement is freely available. We derive a universal additive upper…
We show that almost all known lower bound methods for communication complexity are also lower bounds for the information complexity. In particular, we define a relaxed version of the partition bound of Jain and Klauck and prove that it…
We prove that the entanglement cost equals the regularized entanglement of formation for any infinite-dimensional quantum state $\rho_{AB}$ with finite quantum entropy on at least one of the subsystems $A$ or $B$. This generalizes a…
We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of disjointness. For protocols with $r$ rounds, we prove a lower bound of $\tilde{\Omega}(n/r + r)$ on the communication required for…
A strong direct product theorem states that, in order to solve k instances of a problem, if we provide less than k times the resource required to compute one instance, then the probability of overall success is exponentially small in k. In…
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 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…
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…
The focus of this paper is on {\em quantum distributed} computation, where we investigate whether quantum communication can help in {\em speeding up} distributed network algorithms. Our main result is that for certain fundamental network…
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…
We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state. We prove linear lower bounds for…