Generalized Random Events

Rodrigo Gallego, Lluís Masanes, Gonzalo de la Torre +3 more

Dmitriy A. Klyushin

A new definition of random events is considered in the context of quantum random bit generators. It generalizes the definition of randomness by von Mises and overcomes its deficiencies. We proposed to eliminate the rule for choosing an acceptable place using the characteristic matrix of a random experiment. According to the new model of randomness random events forms an atomic, complete and fully distributive Boolean algebra. It is shown that the probability distribution generated by random variables in this model is not a measure, but only a finite-additive function of events in the case of continuous rational or real random variables. Numerical experiments with quantum random number generators were carried out. Their results have shown that the model is consistent with experimental observations.

Philippe Réfrégier

Tânia Tomé, Mário J. de Oliveira

Ying Guo, Guihua Zeng

To simultaneously detect random and burst quantum errors which may be generalized as quantum event errors, a quantum error detection code, called the quantum event-error detection code, is first investigated in analogy to the classical event-error detection code. The proposed code can be used to detect the length, number and location of errors occurring in every error event. Two special quantum event-error detection codes are constructed by exploiting different approaches according to the derived syndrome, and their number-bound of generators of the stabilizer is also derived. Finally, the proposed theory on the quantum event-error detection code for quantum single-event error is extended to a more general case, i.e., the quantum composite-event error, so that the general quantum event-error detection code can be constructed.

Roberto Piazza