A temporal analogue of information‐theoretic Bell inequalities is formulated for computational processes by considering a series of observables at different time steps. The information‐theoretic temporal Bell inequality offers a novel way of contrasting classical and quantum computations.
A new kind of temporal inequalities are discussed, which apply to algorithmic processes, involving a finite memory processing unit. They are an alternative to the Leggett-Grag ones, as well as to the modified ones by Brukner et al . If one considers comparison of quantum and classical processes involving systems of finite memory (of the same capacity in both cases), the inequalities give a clear message why we can expect quantum speed-up. In a classical process one always has clearly defined values of possible measurements, or in terms of the information processing language, if we have a sequential computations of some function depending on data arriving at each step on an algorithm, the function always has a clearly defined value. In the quantum case only the final value, after the end of the algorithm, is defined. All intermediate values, in agreement with Bohr’s complementarity, cannot be ascribed a definite value.
We formulate information-theoretic Bell inequalities, which apply to any pair of widely separated physical systems. If local realism holds, the two systems must carry information consistent with the inequalities. Two spin-s particles in a state of zero total spin violate these information Bell inequalities.
I: Quantum information obeys laws that subtly extend those governing classical information, making possible novel effect such as cryptography and quantum computation. Quantum computations are extremely sensitive to disruption by interaction of the computer with its environment, but this problem can be overcome by recently developed quantum versions of classical error-correcting codes and fault-tolerant circuits. Based on these ideas, the purpose of this paper is to provide an approach to quantum information by analyzing and demonstrating Bell's inequality and by discussing the problems related to decoherence and error-correcting. II: The growing need for a better understanding of complex processes has stimulated the development of new and more advanced data analysis techniques. The purpose of this research was to investigate some of the already existing techniques (Hurst's rescaled range and relative dispersion analysis), to develop a software able to process time series with these techniques, and to get familiar with the theory of diffusion processes.