Investigation of the influence of measurement imperfections on quantum communication complexity superiority for the Clauser-Horne-Shimony-Holt game

Abstract

Demonstrating quantum communication complexity superiority non-trivially with currently available experimental systems is of utmost importance in quantum information science. Here, we propose a generalized entanglement-assisted communication complexity reduction protocol and analyze the robustness of its quantum superiority against the measurement imperfections, such as measurement basis deviation and choice probability bias, a common problem rarely studied before. We find that the quantum superiority can be obtained in a specific entangled state in a suitable range of measurement basis and basis choice parameters. And the quantum superiority strengthens with the increase of the entanglement degree of quantum states. By using the maximum entangled state and its corresponding optimal measurement, the result we obtained violated the optimal classical bound by 239 standard deviations. Besides, the robustness of effective measurement basis in dephasing and depolarizing quantum channels is also investigated. These results not only make a step forward in investigating sufficient experimental conditions to unambiguously demonstrate the superiority of quantum communication complexity but also help to develop relevant practical applications.