In this paper, we show how information causality leads to Tsirelson bounds in a much easier way. Furthermore, a series of new Tsirelson bounds are then derived. We then define the communication protocols based on Random access code（RAC） and No-signaling box（NS-box） and then derive the objects for the communication complexity of symmetric quantum channels with i.i.d.（independent identically distribution） and uniform input marginal probabilities, consequently we obtain the multi-level Bell-type inequality. Deep ramifications concerning non-local quantum computation are also found and discussed.
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