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A process of preparation, transmission and subsequent projective measurementof a qubit can be simulated by a classical model with only two bits ofcommunication and some amount of shared randomness. However no model for nqubits with a finite amount of classical communication is known at present. Alower bound for the communication cost can provide useful hints for ageneralization. It is known for example that the amount of communication mustbe greater than c 2^n, where c~0.01. The proof uses a quite elaborate theoremof communication complexity. Using a mathematical conjecture known as the"double cap conjecture", we strengthen this result by presenting a geometricaland extremely simple derivation of the lower bound 2^n-1. Only rank-1projective measurements are involved in the derivation.

Communication cost of classically simulating a quantum channel with subsequent rank-1 projective measurement