Classical simulations of quantum prepare and measure communication processes

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Quantum communication has been shown to be vastly superior to classical communication in many problems. However no general statements exist which tells us how much better quantum communication is to its classical counterpart. In this thesis it was studied the minimum amount of classical bits required to exactly simulate a quantum communication process. The quantum communication process specifically studied was a quantum prepare and measurement communication problem. It has been shown that the calculation of the amount of classical bits of communication required for simulation reduces to a minimization-maximization optimization problem. Several results have been presented for for solving this optimization problem and in addition a link was made between classical simulations of quantum communication and a recent debate on the reality of the quantum state.