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We show that any classical two-way communication protocol with shared randomness that can approximately simulate the result of applying an arbitrary measurement (held by one party) to a quantum state of $n$ qubits (held by another), up to…

Quantum Physics · Physics 2019-07-03 Ashley Montanaro

Deterministic and probabilistic communication protocols are introduced in which parties can exchange the values of polynomials (rather than bits in the usual setting). It is established a sharp lower bound $2n$ on the communication…

Computational Complexity · Computer Science 2007-10-16 Dima Grigoriev

This paper studies the one-way communication complexity of the subgroup membership problem, a classical problem closely related to basic questions in quantum computing. Here Alice receives, as input, a subgroup $H$ of a finite group $G$;…

Computational Complexity · Computer Science 2021-10-05 Scott Aaronson , François Le Gall , Alexander Russell , Seiichiro Tani

We resolve the randomized one-way communication complexity of Dynamic Time Warping (DTW) distance. We show that there is an efficient one-way communication protocol using $\widetilde{O}(n/\alpha)$ bits for the problem of computing an…

Data Structures and Algorithms · Computer Science 2019-03-11 Vladimir Braverman , Moses Charikar , William Kuszmaul , David P. Woodruff , Lin F. Yang

The process of state preparation, its transmission and subsequent measurement can be classically simulated through the communication of some amount of classical information. Recently, we proved that the minimal communication cost is the…

Quantum Physics · Physics 2014-01-17 Alberto Montina , Stefan Wolf

We study space-bounded communication complexity for unitary implementation in distributed quantum processors, where we restrict the number of qubits per processor to ensure practical relevance and technical non-triviality. We model…

Quantum Physics · Physics 2025-11-07 Longcheng Li , Xiaoming Sun , Jialin Zhang , Jiadong Zhu

One of the strongest techniques available for showing lower bounds on quantum communication complexity is the logarithm of the approximation rank of the communication matrix--the minimum rank of a matrix which is entrywise close to the…

Computational Complexity · Computer Science 2021-03-09 Troy Lee , Adi Shraibman

This paper gives a nearly tight characterization of the quantum communication complexity of the permutation-invariant Boolean functions. With such a characterization, we show that the quantum and randomized communication complexity of the…

Computational Complexity · Computer Science 2025-10-14 Ziyi Guan , Yunqi Huang , Penghui Yao , Zekun Ye

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…

Computational Complexity · Computer Science 2020-09-08 Arkadev Chattopadhyay , Ankit Garg , Suhail Sherif

The main conceptual contribution of this paper is investigating quantum multiparty communication complexity in the setting where communication is \emph{oblivious}. This requirement, which to our knowledge is satisfied by all quantum…

Quantum Physics · Physics 2023-12-29 François Le Gall , Daiki Suruga

We show that for any Boolean function f on {0,1}^n, the bounded-error quantum communication complexity of XOR functions $f\circ \oplus$ satisfies that $Q_\epsilon(f\circ \oplus) = O(2^d (\log\|\hat f\|_{1,\epsilon} + \log…

Computational Complexity · Computer Science 2013-07-26 Shengyu Zhang

We study the one-clean-qubit model of quantum communication where one qubit is in a pure state and all other qubits are maximally mixed. We demonstrate a partial function that has a quantum protocol of cost $O(\log N)$ in this model,…

Quantum Physics · Physics 2023-10-05 Srinivasan Arunachalam , Uma Girish , Noam Lifshitz

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…

Quantum Physics · Physics 2008-02-03 Richard Cleve , Wim van Dam , Michael Nielsen , Alain Tapp

The Collision problem is to decide whether a given list of numbers $(x_1,\ldots,x_n)\in[n]^n$ is $1$-to-$1$ or $2$-to-$1$ when promised one of them is the case. We show an $n^{\Omega(1)}$ randomised communication lower bound for the natural…

Computational Complexity · Computer Science 2022-08-11 Mika Göös , Siddhartha Jain

Equality and disjointness are two of the most studied problems in communication complexity. They have been studied for both classical and also quantum communication and for various models and modes of communication. Buhrman et al. [Buh98]…

Computational Complexity · Computer Science 2013-10-01 Jozef Gruska , Daowen Qiu , Shenggen Zheng

We study the round and communication complexities of various cryptographic protocols. We give tight lower bounds on the round and communication complexities of any fully black-box reduction of a statistically hiding commitment scheme from…

Cryptography and Security · Computer Science 2021-05-05 Iftach Haitner , Jonathan J. Hoch , Omer Reingold , Gil Segev

We study the communication complexity of symmetric XOR functions, namely functions $f: \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}$ that can be formulated as $f(x,y)=D(|x\oplus y|)$ for some predicate $D: \{0,1,...,n\} \rightarrow…

Computational Complexity · Computer Science 2011-11-01 Ming Lam Leung , Yang Li , Shengyu Zhang

We study a model of communication complexity that encompasses many well-studied problems, including classical and quantum communication complexity, the complexity of simulating distributions arising from bipartite measurements of shared…

Quantum Physics · Physics 2011-07-08 Julien Degorre , Marc Kaplan , Sophie Laplante , Jérémie Roland

We study nondeterministic quantum algorithms for Boolean functions f. Such algorithms have positive acceptance probability on input x iff f(x)=1. In the setting of query complexity, we show that the nondeterministic quantum complexity of a…

Computational Complexity · Computer Science 2007-05-23 Ronald de Wolf

We consider the problem of testing whether a Boolean function has Fourier degree $\leq k$ or it is $\epsilon$-far from any Boolean function with Fourier degree $\leq k$. We improve the known lower bound of $\Omega(k)$ \cite{BBM11,CGM10}, to…

Computational Complexity · Computer Science 2013-08-27 Pooya Hatami