相关论文: Lower bounds for quantum communication complexity

We describe new lower bounds for randomized communication complexity and query complexity which we call the partition bounds. They are expressed as the optimum value of linear programs. For communication complexity we show that the…

In this paper we prove lower bounds on randomized multiparty communication complexity, both in the \emph{blackboard model} (where each message is written on a blackboard for all players to see) and (mainly) in the \emph{message-passing…

Quantum entanglement cannot be used to achieve direct communication between remote parties, but it can reduce the communication needed for some problems. Let each of k parties hold some partial input data to some fixed k-variable function…

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…

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…

In some scenarios there are ways of conveying information with many fewer, even exponentially fewer, qubits than possible classically. Moreover, some of these methods have a very simple structure--they involve only few message exchanges…

We prove an optimal $\Omega(n)$ lower bound on the randomized communication complexity of the much-studied Gap-Hamming-Distance problem. As a consequence, we obtain essentially optimal multi-pass space lower bounds in the data stream model…

The focus of this paper is on {\em quantum distributed} computation, where we investigate whether quantum communication can help in {\em speeding up} distributed network algorithms. Our main result is that for certain fundamental network…

We put forward a Quantum Amplitude Estimation algorithm delivering superior performance (lower quantum computational complexity and faster classical computation parts) compared to the approaches available to-date. The algorithm does not…

We obtain a general connection between a quantum advantage in communication complexity and non-locality. We show that given any protocol offering a (sufficiently large) quantum advantage in communication complexity, there exists a way of…

The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…

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…

We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input, we use a quantum adversary that runs the algorithm with a…

In this work we introduce an intermediate setting between quantum nonlocality and communication complexity problems. More precisely, we study the value of XOR games $G$ when Alice and Bob are allowed to use a limited amount of one-way…

We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…

Shor's and Grover's famous quantum algorithms for factoring and searching show that quantum computers can solve certain computational problems significantly faster than any classical computer. We discuss here what quantum computers_cannot_…

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 prove a direct sum theorem for bounded round entanglement-assisted quantum communication complexity. To do so, we use the fully quantum definition for information cost and complexity that we recently introduced, and use both the fact…

We define a quantum model for multiparty communication complexity and prove a simulation theorem between the classical and quantum models. As a result of our simulation, we show that if the quantum k-party communication complexity of a…

We introduce a new quantum decoder based on a variant of the pretty good measurement, but defined via an alternative matrix quotient. We use this decoder to show new lower bounds on the error exponent both in the one-shot and asymptotic…