相关论文: Improved Quantum Communication Complexity Bounds f…

The results showing a quantum query complexity of $\Theta(N^{1/3})$ for the collision problem do not apply to random functions. The issues are two-fold. First, the $\Omega(N^{1/3})$ lower bound only applies when the range is no larger than…

The question of how much communication is required between collaborating parties to compute a function of their data is of fundamental importance in the fields of theoretical computer science and information theory. In this work, the focus…

We investigate one-way communication scenarios where Bob manipulating on his parts can transfer some sub-system to the environment. We define reduced versions of quantum communication rates and further, prove new upper bounds on one-way…

We investigate query-to-communication lifting theorems for models related to the quantum adversary bounds. Our results are as follows: 1. We show that the classical adversary bound lifts to a lower bound on randomized communication…

The collision problem is to decide whether a function X:{1,..,n}->{1,..,n} is one-to-one or two-to-one, given that one of these is the case. We show a lower bound of Theta(n^{1/5}) on the number of queries needed by a quantum computer to…

We study the quantum query complexity of two problems. First, we consider the problem of determining if a sequence of parentheses is a properly balanced one (a Dyck word), with a depth of at most $k$. We call this the $Dyck_{k,n}$ problem.…

I present a simple two-party quantum communication complexity protocol with higher success rate than the best possible classical protocol for the same task. The quantum protocol is shown to be equivalent to a quantum non-locality test,…

We study two basic graph parameters, the chromatic number and the orthogonal rank, in the context of classical and quantum exact communication complexity. In particular, we consider two types of communication problems that we call promise…

We fully determine the communication complexity of approximating matrix rank, over any finite field $\mathbb{F}$. We study the most general version of this problem, where $0\leq r<R\leq n$ are given integers, Alice and Bob's inputs are…

In this work we focus our attention on distributed optimization problems in the context where the communication time between the server and the workers is non-negligible. We obtain novel methods supporting bidirectional compression (both…

Quantum systems are known to offer advantages over their classical counterpart in communication complexity protocols, where the aim is to minimize the amount of information exchange between distant parties to compute global functions of…

It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of…

We give improved separations for the query complexity analogue of the log-approximate-rank conjecture i.e. we show that there are a plethora of total Boolean functions on $n$ input bits, each of which has approximate Fourier sparsity at…

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…

We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved,…

In this paper we obtain some bounds on communication complexity of Gap Hamming Distance problem ($\mathsf{GHD}^n_{L, U}$): Alice and Bob are given binary string of length $n$ and they are guaranteed that Hamming distance between their…

We use techniques for lower bounds on communication to derive necessary conditions in terms of detector efficiency or amount of super-luminal communication for being able to reproduce with classical local hidden-variable theories the…

We present a new decoding protocol to realize transmission of classical information through a quantum channel at asymptotically maximum capacity, achieving the Holevo bound and thus the optimal communication rate. At variance with previous…

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…

We introduce a quantum packing bound on the minimal resources required by nondegenerate error correction codes for any kind of noise. We prove that degenerate codes can outperform nondegenerate ones in the presence of correlated noise, by…