Certifying the classical simulation cost of a quantum channel

A fundamental objective in quantum information science is to determine the cost classical resources of simulating a particular system. The simulation quantified by signaling dimension which specifies minimum amount communication needed perfectly simulate channel's input-output correlations when unlimited shared randomness held between encoder and decoder. This paper provides collection device-independent tests that place lower upper bounds on channel. Among them, single family shown noisy channel can be simulated using an strictly less than either its input or output alphabet size. In addition, eight witnesses presented completely characterize any four-outcome measurement channel, such as Bell measurement, one bit randomness. Finally, we bound for all partial replacer channels $d$ dimensions. are found tight special case erasure