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Lecture notes in computer science

Multi-party Quantum Communication Complexity with Routed Messages

Seiichiro Tani, Masaki Nakanishi, Shigeru Yamashita

Published Aug 12, 2008• 0 citations
Publisher
DOI
10.1007/978-3-540-69733-6_19

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This paper describes a general quantum lower bounding technique for the communication complexity of a function that depends on the inputs given to two parties connected via paths, which may be shared with other parties, on a network of any topology. The technique can also be employed to obtain a lower-bound of the quantum communication complexity of some functions that depend on the inputs distributed over all parties on the network. As a typical application, we apply our technique to the distinctness problem of deciding whether there are a pair of parties with identical inputs, on a k-party ring; almost matching upper bounds are also given.
Quantum direct communication (QDC) uses the basic principle of quantum mechanics to realize the secure communication between legal parties. Deterministic secure quantum communication (DSQC), as a branch of QDC, is a way to transmit secret message with the aid of classical bits. In this paper, a multi-party DSQC based on [Formula: see text]-dimension [Formula: see text]-particles GHZ states is proposed, in which unitary operation is not required. On the basis of [Formula: see text]-dimension single-photon measurement results, the communication parties encode and decode the message through performing modulo addition and subtraction. In addition, the scheme uses the added [Formula: see text]-dimension single photon for eavesdropping detection. The scheme has expansibility and universality. It can scale to as many parties in any dimension as required. Based on the star-shaped communication structure, it can be extended to a network to achieve the rapid communication of secret message across regions.