Related papers: On Arthur Merlin Games in Communication Complexity
We introduce and study the communication complexity of computing the inner product of two vectors, where the input is restricted w.r.t. a norm $N$ on the space $\mathbb{R}^n$. Here, Alice and Bob hold two vectors $v,u$ such that $\|v\|_N\le…
This paper studies a generalization of multi-prover interactive proofs in which a verifier interacts with two competing teams of provers: one team attempts to convince the verifier to accept while the other attempts to convince the verifier…
We consider the process consisting of preparation, transmission through a quantum channel, and subsequent measurement of quantum states. The communication complexity of the channel is the minimal amount of classical communication required…
We give lower bounds on the communication complexity required to solve several computational problems in a distributed-memory parallel machine, namely standard matrix multiplication, stencil computations, comparison sorting, and the Fast…
This work addresses two problems in the context of two-party communication complexity of functions. First, it concludes the line of research, which can be viewed as demonstrating qualitative advantage of quantum communication in the three…
A two-party quantum communication process with classical inputs and outcomes can be simulated by replacing the quantum channel with a classical one. The minimal amount of classical communication required to reproduce the statistics of the…
Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only…
We propose a protocol for Alice to implement a multiqubit quantum operation from the restricted sets on distant qubits possessed by Bob, and then we investigate the communication complexity of the task in different communication scenarios.…
We prove new bounds on the quantum communication complexity of the disjointness and equality problems. For the case of exact and non-deterministic protocols we show that these complexities are all equal to n+1, the previous best lower bound…
This paper studies multiple-proof quantum Merlin-Arthur (QMA) proof systems in the setting when the completeness-soundness gap is small. Small means that we only lower-bound the gap with an inverse-exponential function of the input length,…
We present a new example of a partial boolean function whose one-way quantum communication complexity is exponentially lower than its one-way classical communication complexity. The problem is a natural generalisation of the previously…
In this paper the Neciporuk method for proving lower bounds on the size of Boolean formulae is reformulated in terms of one-way communication complexity. We investigate the scenarios of probabilistic formulae, nondeterministic formulae, and…
Evaluating higher-order functional programs through abstract machines inspired by the geometry of the interaction is known to induce $\textit{space}$ efficiencies, the price being $\textit{time}$ performances often poorer than those…
We demonstrate a two-player communication problem that can be solved in the one-way quantum model by a 0-error protocol of cost O (log n) but requires exponentially more communication in the classical interactive (bounded error) model.
We present a classical interactive protocol that verifies the validity of a quantum witness state for the local Hamiltonian problem. It follows from this protocol that approximating the non-local value of a multi-player one-round game to…
We consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap quantum advantages for communication. For an arbitrary protocol with $n$ messages,…
Alice and Bob want to know if two strings of length n are almost equal. That is, do they differ on \textit{at most} a bits? Let 0\leq a\leq n-1. We show that any deterministic protocol, as well as any error-free quantum protocol (C*…
We study the MARINA method of Gorbunov et al (2021) -- the current state-of-the-art distributed non-convex optimization method in terms of theoretical communication complexity. Theoretical superiority of this method can be largely…
Quantum entanglement, perhaps the most non-classical manifestation of quantum information theory, cannot be used to transmit information between remote parties. Yet, it can be used to reduce the amount of communication required to process a…
We study a new type of separation between quantum and classical communication complexity which is obtained using quantum protocols where all parties are efficient, in the sense that they can be implemented by small quantum circuits with…