Multiparty Quantum Communication Complexity of Triangle Finding
نویسندگان
چکیده
Triangle finding (deciding if a graph contains a triangle or not) is a central problem in quantum query complexity. The quantum communication complexity of this problem, where the edges of the graph are distributed among the players, was considered recently by Ivanyos et al. in the twoparty setting. In this paper we consider its k-party quantum communication complexity with k ≥ 3. Our main result is a Õ(m7/12)-qubit protocol, for any constant number of players k, deciding with high probability if a graph with m edges contains a triangle or not. Our approach makes connections between the multiparty quantum communication complexity of triangle finding and the quantum query complexity of graph collision, a well-studied problem in quantum query complexity. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems
منابع مشابه
Quantum Multiparty Communication Complexity and Circuit Lower Bounds
We define a quantum model for multiparty communication complexity and prove a simulation theorem between the classical and quantum models. As a result, we show that if the quantum k-party communication complexity of a function f is Ω( n 2k ), then its classical k-party communication is Ω( n 2k/2 ). Finding such an f would allow us to prove strong classical lower bounds for k ≥ log n players and...
متن کاملOn the Multiparty Communication Complexity of Testing Triangle-Freeness
In this paper we initiate the study of property testing in simultaneous and non-simultaneous multi-party communication complexity, focusing on testing triangle-freeness in graphs. We consider the coordinator model, where we have k players receiving private inputs, and a coordinator who receives no input; the coordinator can communicate with all the players, but the players cannot communicate wi...
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 کاملTensor Rank and Strong Quantum Nondeterminism in Multiparty Communication
In this paper we study quantum nondeterminism in multiparty communication. There are three (possibly) different types of nondeterminism in quantum computation: i) strong, ii) weak with classical proofs, and iii) weak with quantum proofs. Here we focus on the first one. A strong quantum nondeterministic protocol accepts a correct input with positive probability, and rejects an incorrect input wi...
متن کامل/ 04 09 19 1 v 2 10 F eb 2 00 5 Proposed experiment for the quantum “ Guess My Number ” protocol
An experimental realization of the entanglement-assisted “Guess My Number” protocol for the reduction of communication complexity, introduced by Steane and van Dam, would require producing and detecting three-qubit GHZ states with an efficiency η > 0.70, which would require single photon detectors of efficiency σ > 0.89. We propose a modification of the protocol which can be translated into a r...
متن کامل