title: Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication.
abstract: In communication complexity, a number of distant parties have the task of calculating a distributed function of their inputs, while minimizing the amount of communication between them. It is known that with quantum resources, such as entanglement and quantum channels, one can obtain significant reductions in the communication complexity of some tasks. In this work, we study the role of the quantum superposition of the direction of communication as a resource for communication complexity. We present a tripartite communication task for which such a superposition allows for an exponential saving in communication, compared to one-way quantum (or classical) communication; the advantage also holds when we allow for protocols with bounded error probability.
authors.affiliation: Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria and Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria.
authors.forename: Philippe Allard
authors.initials: PA
authors.lastname: Guérin
authors.affiliation: Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria and Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria.
authors.forename: Adrien
authors.initials: A
authors.lastname: Feix
authors.affiliation: Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria and Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria.
authors.forename: Mateus
authors.initials: M
authors.lastname: Araújo
authors.affiliation: Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria and Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria.
authors.forename: Časlav
authors.initials: Č
authors.lastname: Brukner