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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…

Quantum Physics · Physics 2018-02-13 Harry Buhrman , Matthias Christandl , Jeroen Zuiddam

We use critical block sensitivity, a new complexity measure introduced by Huynh and Nordstr\"om (STOC 2012), to study the communication complexity of search problems. To begin, we give a simple new proof of the following central result of…

Computational Complexity · Computer Science 2016-07-12 Mika Göös , Toniann Pitassi

We consider a natural generalization of an abelian Hidden Subgroup Problem where the subgroups and their cosets correspond to graphs of linear functions over a finite field F with d elements. The hidden functions of the generalized problem…

Quantum Physics · Physics 2008-09-02 Thomas Decker , Jan Draisma , Pawel Wocjan

Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…

Quantum Physics · Physics 2023-05-16 Ashley Montanaro , Changpeng Shao

We determine the covert capacity for entanglement generation over a noisy quantum channel. While secrecy guarantees that the transmitted information remains inaccessible to an adversary, covert communication ensures that the transmission…

Quantum Physics · Physics 2026-05-27 Ohad Kimelfeld , Boulat A. Bash , Uzi Pereg

Computing set joins of two inputs is a common task in database theory. Recently, Van Gucht, Williams, Woodruff and Zhang [PODS 2015] considered the complexity of such problems in the natural model of (classical) two-party communication…

Quantum Physics · Physics 2016-08-24 Stacey Jeffery , François Le Gall

We prove that the fidelity of two exemplary communication complexity protocols, allowing for an N-1 bit communication, can be exponentially improved by N-1 (unentangled) qubit communication. Taking into account, for a fair comparison, all…

Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient…

Quantum Physics · Physics 2025-01-15 Nikhil S. Mande , Changpeng Shao

Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known "entanglement…

Quantum Physics · Physics 2022-03-29 Dmytro Gavinsky

We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…

Quantum Physics · Physics 2021-09-22 Mark Bun , Robin Kothari , Justin Thaler

Communication complexity is the amount of communication needed to compute a function when the function inputs are distributed over multiple parties. In its simplest form, one-way communication complexity, Alice and Bob compute a function…

Computational Complexity · Computer Science 2023-05-24 Naresh Goud Boddu , Rahul Jain , Han-Hsuan Lin

We explore covert communication of qubits over an arbitrary quantum channel. Covert communication conceals the transmissions in the channel noise, ensuring that an adversary is unable to detect their presence. We show the achievability of a…

Quantum Physics · Physics 2025-01-28 Evan J. D. Anderson , Michael S. Bullock , Filip Rozpędek , Boulat A. Bash

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,…

Quantum Physics · Physics 2020-01-10 Debbie Leung , Ashwin Nayak , Ala Shayeghi , Dave Touchette , Penghui Yao , Nengkun Yu

We propose a linear algebraic method, rooted in the spectral properties of graphs, that can be used to prove lower bounds in communication complexity. Our proof technique effectively marries spectral bounds with information-theoretic…

Information Theory · Computer Science 2024-04-16 Geoffroy Caillat-Grenier , Andrei Romashchenko

We call $F:\{0, 1\}^n\times \{0, 1\}^n\to\{0, 1\}$ a symmetric XOR function if for a function $S:\{0, 1, ..., n\}\to\{0, 1\}$, $F(x, y)=S(|x\oplus y|)$, for any $x, y\in\{0, 1\}^n$, where $|x\oplus y|$ is the Hamming weight of the bit-wise…

Quantum Physics · Physics 2008-08-20 Yaoyun Shi , Zhiqiang Zhang

Representations of Boolean functions by real polynomials play an important role in complexity theory. Typically, one is interested in the least degree of a polynomial p(x_1,...,x_n) that approximates or sign-represents a given Boolean…

Computational Complexity · Computer Science 2008-05-15 Alexander A. Sherstov

We study the weakest model of quantum nondeterminism in which a classical proof has to be checked with probability one by a quantum protocol. We show the first separation between classical nondeterministic communication complexity and this…

Quantum Physics · Physics 2021-10-05 Francois Le Gall

A fundamental problem in computer science is to find all the common zeroes of $m$ quadratic polynomials in $n$ unknowns over $\mathbb{F}_2$. The cryptanalysis of several modern ciphers reduces to this problem. Up to now, the best complexity…

Symbolic Computation · Computer Science 2015-03-19 Magali Bardet , Jean-Charles Faugère , Bruno Salvy , Pierre-Jean Spaenlehauer

The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…

Quantum Physics · Physics 2020-02-12 Avishay Tal

Bell's theorem implies that the outcomes of local measurements on two maximally entangled systems cannot be simulated without classical communication between the parties. The communication cost is finite for n Bell states, but it grows…

Quantum Physics · Physics 2011-10-17 Alberto Montina