Abstract
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 at least two parties with identical inputs, on a k-party ring; almost matching upper bounds are also given.
This work was supported in part by Grant-in-Aid for Scientific Research (KAKENHI): (16092218), (18700011), (19700010) and (19700019).
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Tani, S., Nakanishi, M., Yamashita, S. (2008). Multi-party Quantum Communication Complexity with Routed Messages. In: Hu, X., Wang, J. (eds) Computing and Combinatorics. COCOON 2008. Lecture Notes in Computer Science, vol 5092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69733-6_19
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DOI: https://doi.org/10.1007/978-3-540-69733-6_19
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