Multi-level Bell-Type Inequality from Information Causality and Noisy Computations

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.