Quantum Communication Complexity
نویسنده
چکیده
This paper surveys the field of quantum communication complexity. Some interesting recent results are collected concerning relations to classical communication, lower bound methods, one-way communication, and applications of quantum communication complexity.
منابع مشابه
Lower Bounds for Quantum Communication Complexity
We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower bounds developed by Raz [30] to the quantum case. Applying this method we give an exponential separation between bounded error quantum communication complexity a...
متن کاملCommunication complexity of promise problems and their applications to finite automata
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. [6] proved that the exact quantum communication complexity for a promise version of the equality problem is O(logn) while the classical deterministic communication co...
متن کاملExponential Quantum-Classical Gaps in Multiparty Nondeterministic Communication Complexity
There are three different types of nondeterminism in quantum communication: i) NQP-communication, ii) QMA-communication, and iii) QCMA-communication. In this paper we show that multiparty NQP-communication can be exponentially stronger than QCMA-communication. This also implies an exponential separation with respect to classical multiparty nondeterministic communication complexity. We argue tha...
متن کاملThe Corruption Bound, Log Rank, and Communication Complexity
We prove that for every sign matrix A there is a deterministic communication protocol that uses O(corr1/4(A) log 2 rank(A)) bits of communication, where corr1/4(A) is the corruption/rectangle bound with error 1/4. This bound generalizes several of the known upper bounds on deterministic communication complexity, involving nondeterministic complexity, randomized complexity, information complexit...
متن کاملDirect Sum Theorem for Bounded Round Quantum Communication Complexity
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 that information is a lower bound on communication, and the fact that a direct sum property holds for quantum information complexity. We then give a protocol fo...
متن کامل