A New Approach for Estimating the Rate of Emission in Quantum Bit Exchange‏ ‎Systems ‎Using Binomial Distribution

Information ‎theoretic ‎bit ‎exchange ‎algorithms ‎are ‎usually evaluated ‎by their ‎‎efficiency, which is the number of successfully received bits with respect to the number of sent bits. Though, this is also the case in the quantum version of the information theory, another indicator can be derived based on it, to give a view of the costs of the algorithm. This indicator is simply the number of qubits that must be sent to obtain a   desired bit string. Depending on the expected length of the output of the algorithm, this indicator reveals more detailed information about the number of qubits that must be emitted, and better estimates the        implementation costs, while efficiency is an indicator that can evaluate algorithms only theoretically. We employed the idea of overselling in a transportation ticketing scheme to illustrate how to apply the binomial distribution to calculate the alternative indicator. The scheme is first reworded to fit the concepts and     notations of a quantum information encoding system based on the double-slit experiment; typical results  are represented. Finally, the scheme is applied to the QKD protocols such as BB84 and Six-State, for  calculating the number of qubits necessary to send in order to obtain a key of the desired length, in terms of the error rate.