Related papers: Distributed Quantum Advantage in Locally Checkable…
In this work we introduce the graph-theoretic notion of mendability: for each locally checkable graph problem we can define its mending radius, which captures the idea of how far one needs to modify a partial solution in order to "patch a…
There is currently a large interest in understanding the potential advantages quantum devices can offer for probabilistic modelling. In this work we investigate, within two different oracle models, the probably approximately correct (PAC)…
We study the advantages of quantum communication models over classical communication models that are equipped with a limited number of qubits of entanglement. In this direction, we give explicit partial functions on $n$ bits for which…
The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…
In the study of deterministic distributed algorithms it is commonly assumed that each node has a unique $O(\log n)$-bit identifier. We prove that for a general class of graph problems, local algorithms (constant-time distributed algorithms)…
We propose the task of local state marking (LSM), where some multipartite quantum states chosen randomly from a known set of states are distributed among spatially separated parties without revealing the identities of the individual states.…
Distributed quantum information processing protocols such as quantum entanglement distillation and quantum state discrimination rely on local operations and classical communications (LOCC). Existing LOCC-based protocols typically assume the…
This paper studies the limitations of the generic approaches to solving cryptographic problems in classical and quantum settings in various models. - In the classical generic group model (GGM), we find simple alternative proofs for the…
The All-Pairs Shortest Path problem (APSP) is one of the most central problems in distributed computation. In the CONGEST-CLIQUE model, in which $n$ nodes communicate with each other over a fully connected network by exchanging messages of…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
The local Hamiltonian (LH) problem, the quantum analog of the classical constraint satisfaction problem, is a cornerstone of quantum computation and complexity theory. It is known to be QMA-complete, indicating that it is challenging even…
In this paper, we present a low-diameter decomposition algorithm in the LOCAL model of distributed computing that succeeds with probability $1 - 1/poly(n)$. Specifically, we show how to compute an $\left(\epsilon, O\left(\frac{\log…
In this paper, we mainly study the local distinguishable multipartite quantum states by local operations and classical communication (LOCC) in $m_1\otimes m_2\otimes\ldots\otimes m_n$ , where the quantum system $m_1$ belongs to Alice, $m_2$…
We present new randomized algorithms that improve the complexity of the classic $(\Delta+1)$-coloring problem, and its generalization $(\Delta+1)$-list-coloring, in three well-studied models of distributed, parallel, and centralized…
In the past few years, a successful line of research has lead to lower bounds for several fundamental local graph problems in the distributed setting. These results were obtained via a technique called round elimination. On a high level,…
This paper gives the first separation of quantum and classical pure (i.e., non-cryptographic) computing abilities with no restriction on the amount of available computing resources, by considering the exact solvability of a celebrated…
We present improved deterministic distributed algorithms for a number of well-studied matching problems, which are simpler, faster, more accurate, and/or more general than their known counterparts. The common denominator of these results is…
By prior work, there is a distributed algorithm that finds a maximal fractional matching (maximal edge packing) in $O(\Delta)$ rounds, where $\Delta$ is the maximum degree of the graph. We show that this is optimal: there is no distributed…
A standard model in network synchronised distributed computing is the LOCAL model. In this model, the processors work in rounds and, in the classic setting, they know the number of vertices of the network, $n$. Using $n$, they can compute…
The locality of a graph problem is the smallest distance $T$ such that each node can choose its own part of the solution based on its radius-$T$ neighborhood. In many settings, a graph problem can be solved efficiently with a distributed or…