Related papers: Quantum Log-Approximate-Rank Conjecture is also Fa…
Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable…
Numbers-on-Forehead (NOF) communication model is a central model in communication complexity. As a restricted variant, one-way NOF model is of particular interest. Establishing strong one-way NOF lower bounds would imply circuit lower…
We study nondeterministic multiparty quantum communication with a quantum generalization of broadcasts. We show that, with number-in-hand classical inputs, the communication complexity of a Boolean function in this communication model…
Finding exponential separation between quantum and classical information tasks is like striking gold in quantum information research. Such an advantage is believed to hold for quantum computing but is proven for quantum communication…
The field of quantum communications promises the faithful distribution of quantum information, quantum entanglement, and absolutely secret keys, however, the highest rates of these tasks are fundamentally limited by the transmission…
We prove a general lower bound of quantum decision tree complexity in terms of some entropy notion. We regard the computation as a communication process in which the oracle and the computer exchange several rounds of messages, each round…
We study randomized and quantum efficiency lower bounds in communication complexity. These arise from the study of zero-communication protocols in which players are allowed to abort. Our scenario is inspired by the physics setup of Bell…
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…
The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan. At the end of the first section I examine tree-balancing. In the second section I summarize the…
In this paper we study quantum nondeterminism in multiparty communication. There are three (possibly) different types of nondeterminism in quantum computation: i) strong, ii) weak with classical proofs, and iii) weak with quantum proofs.…
This work focuses on understanding the quantum message complexity of two central problems in distributed computing, namely, leader election and agreement in synchronous message-passing communication networks. We show that quantum…
We give an exponential separation between one-way quantum and classical communication complexity for a Boolean function. Earlier such a separation was known only for a relation. A very similar result was obtained earlier but independently…
In quantum mechanics, a fundamental law prevents quantum communications to simultaneously achieve high rates and long distances. This limitation is well known for point-to-point protocols, where two parties are directly connected by a…
The communication complexity of many fundamental problems reduces greatly when the communicating parties share randomness that is independent of the inputs to the communication task. Natural communication processes (say between humans)…
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…
It has long been known that the existence of certain superquantum nonlocal correlations would cause communication complexity to collapse. The absurdity of a world in which any nonlocal binary function could be evaluated with a constant…
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 introduce a new information-theoretic complexity measure $IC_\infty$ for 2-party functions which is a lower-bound on communication complexity, and has the two leading lower-bounds on communication complexity as its natural relaxations:…
Quantum communication typically involves a linear chain of repeater stations, each capable of reliable local quantum computation and connected to their nearest neighbors by unreliable communication links. The communication rate in existing…
We present new distributed quantum algorithms for fundamental distributed computing problems, namely, leader election, broadcast, Minimum Spanning Tree (MST), and Breadth-First Search (BFS) tree, in arbitrary networks. These algorithms are…